Question 1

Solve. Round to the nearest tenth.
-One end guy wire is attached to the top of a 22-foot pole and the other end is anchored into the ground 16 feet from the base of the pole. Find the length of the guy wire. 
A)27.2 ft
B)38 ft
C)38.2 ft
D)27 ft

Accepted Answer

The answer of Solve. Round to the nearest tenth.
-One end...

Question 2

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest
thousandth.
-leg = 8, leg = 3
A)3.317
B)7.416
C)2.236
D)8.544

Accepted Answer

This is a right triangle, so we can use the Pythagorean Theorem to find the length of the hypotenuse (the side not given).

c^2 = a^2 + b^2

c^2 = 8^2 + 3^2

c^2 = 64 + 9

c^2 = 73

c ≈ 8.544 (rounded to the nearest thousandth)

Therefore, the best choice is D) 8.544 Using the Pythagorean Theorem, we can find the length of the hypotenuse: 
$c^2=a^2+b^2$
$c^2=8^2+3^2$
$c^2=64+9$
$c^2=73$
$c=\sqrt{73}$
$c\approx8.544$

Question 3

Determine whether the pair of triangles is congruent.
-
A)congruent
B)not congruent

Accepted Answer

We cannot determine whether the triangles are congruent without additional information. The given image only shows two separate triangles with no indication of any congruent sides or angles. It is not possible to determine whether the triangles are congruent based on the given information. There are no measurements or angles provided, so we cannot use any of the congruence criteria to determine if they are congruent.

Question 4

Determine whether the pair of triangles is congruent.
-
A)congruent
B)not congruent

Accepted Answer

The answer of Determine whether the pair of triangles is...

Question 5

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest
thousandth.
-leg = 7, hypotenuse = 14
A)15.652
B)12.124
C)4.583
D)2.646

Accepted Answer

The answer of Sketch the right triangle and find the...

Question 6

Solve. Round to the nearest tenth.
-A 30-ft-tall ladder is placed so that it reaches 19 ft up on the wall of a house. How far is the base of the ladder from the wall of the house? 
A)23.2 ft
B)1261 ft
C)539 ft
D)35.5 ft

Accepted Answer

Using the Pythagorean Theorem, we can find the distance from the wall to the base of the ladder:

(distance from the wall)^2 + (height of ladder)^2 = (length of ladder)^2

x^2 + 19^2 = 30^2

x^2 + 361 = 900

x^2 = 539

x ≈ 23.2

So, the base of the ladder is approximately 23.2 feet from the wall. Rounded to the nearest tenth, the answer is A) 23.2 ft. Using the Pythagorean theorem, we have:
(Base Distance)^2 + (Wall Height)^2 = (Ladder Length)^2
(Base Distance)^2 + 19^2 = 30^2
(Base Distance)^2 = 30^2 - 19^2
(Base Distance) ≈ 23.2 ft (rounded to the nearest tenth)

Question 7

Determine whether the pair of triangles is congruent.
-
A)congruent
B)not congruent

Accepted Answer

The answer of Determine whether the pair of triangles is...

Question 8

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest
thousandth.
-leg = 5, hypotenuse = 13
A)12
B)4.243
C)13.928
D)2.828

Accepted Answer

The answer of Sketch the right triangle and find the...

Question 9

Solve. Round to the nearest tenth.
-A rectangular plot of land is 84 meters wide by 92 meters long. Find the length of the diagonal and if necessary, round to the nearest tenth meter. 
A)124.6 m
B)126.5 m
C)176 m
D)37.5 m

Accepted Answer

The answer of Solve. Round to the nearest tenth.
-A rectangular...

Question 10

Solve. Round to the nearest tenth.
-Juliet runs out of gas in Barnhaven, South Carolina. She walks 8 mi west and then 3 mi south looking for a gas station. How far is she from her starting point?
A)3.3 mi
B)7.4 mi
C)73 mi
D)8.5 mi

Accepted Answer

This problem can be solved using the Pythagorean theorem. The distance Juliet is from her starting point is the hypotenuse of a right triangle with legs of 3 miles and 8 miles. So, using the Pythagorean theorem:

distance = sqrt(3^2 + 8^2)
distance = sqrt(9 + 64)
distance = sqrt(73)

Rounding to the nearest tenth, distance = 8.5. Therefore, the answer is D.

Question 11

Solve. Round to the nearest tenth.
-A 12-foot ladder is leaning against a house with the base of the ladder 4 feet from the house. How high up the house does the ladder reach? If necessary, round to the nearest tenth foot. 
A)11.3 ft
B)11.8 ft
C)12.6 ft
D)8 ft

Accepted Answer

This problem involves finding the length of the ladder, which is the hypotenuse of a right triangle. Using the Pythagorean Theorem, we have:

ladder^2 = 12^2 + 4^2
ladder^2 = 144 + 16
ladder^2 = 160
ladder ≈ 12.65

Rounding to the nearest tenth, we get the ladder reaches approximately 11.3 feet up the house. Therefore, the best choice is A. Using the Pythagorean theorem, we can find the height of the ladder:
h^2 = 12^2 - 4^2
h^2 = 144 - 16
h^2 = 128
h ≈ 11.3
Therefore, the ladder reaches a height of approximately 11.3 feet up the house. Rounded to the nearest tenth, the answer is A) 11.3 ft.

Question 12

Solve. Round to the nearest tenth.
-Shane is flying his kite on 38 yd of string. The kite is directly above the edge of a pond. The edge of a pond is 26 yd from where the kite is tied to the ground. How far is the kite above the pond?
A)768 yd
B)27.7 yd
C)2120 yd
D)46 yd

Accepted Answer

We can use the Pythagorean theorem to solve for the height of the kite above the pond.

The length of one side of the right triangle is 26 yd, and the length of the hypotenuse is the length of the kite string, which is 38 yd.

So, we can use the Pythagorean theorem to solve for the height of the kite above the ground:

h^2 + 26^2 = 38^2
h^2 = 38^2 - 26^2
h^2 = 900
h = √900
h = 30

Therefore, the height of the kite above the pond is approximately 30 yards. Rounding to the nearest tenth, we get 27.7 yards. This problem is asking us to find the height of the kite above the pond, which is the same as the length of the perpendicular segment from the kite to the ground. We can use the Pythagorean Theorem to solve for this length:

a² + b² = c²

where a = 26 yd (the distance from the kite to the pond), b = the height of the kite above the pond (what we're trying to find), and c = 38 yd (the length of the string).

So,

26² + b² = 38²

676 + b² = 1444

b² = 768

b ≈ 27.7

Therefore, the kite is about 27.7 yards above the pond. Choice (B) is the best answer.

Question 13

Solve. Round to the nearest tenth.
-Scott set up a volleyball net in his backyard. One of the poles, which forms a right angle with the ground, is 7 feet high. To secure the pole, he attached a rope from the top of the pole to a stake 3 feet from the bottom of the
Pole. To the nearest tenth of a foot, find the length of the rope.
A)6.3 ft.
B)3.2 ft.
C)7.6 ft.
D)58 ft.

Accepted Answer

This question involves the use of the Pythagorean theorem to find the length of the rope. The pole, the rope, and the ground form a right triangle. The height of the pole is the length of one leg of the triangle and the distance from the stake to the pole is the length of the other leg. Using the Pythagorean theorem, we can find the length of the rope:

r^2 = h^2 + d^2

r^2 = 7^2 + 3^2

r^2 = 58

r ≈ 7.6

Therefore, the length of the rope is approximately 7.6 feet, which rounds to 1 decimal place as answer C, 7.6 ft. Using the Pythagorean theorem, we can find the length of the rope:
$length\,of\,rope=\sqrt{(7\,ft)^2+(4\,ft)^2}=7.6\,ft$
Therefore, the nearest tenth of a foot is 7.6 ft, which corresponds to choice C.

Question 14

Determine whether the pair of triangles is congruent.
-
A)not congruent
B)congruent

Accepted Answer

The triangles have different angles and side lengths, indicating that they are not congruent. The triangles have different side lengths and angles. While both have a right angle and a common side length (4), the other side lengths and angles are different. Therefore, they are not congruent.

Question 15

Determine whether the pair of triangles is congruent.
-
A)not congruent
B)congruent

Accepted Answer

The answer of Determine whether the pair of triangles is...

Question 16

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest
thousandth.
-leg = 16, leg = 12
A)2
B)20
C)5.292
D)10.583

Accepted Answer

The length of the hypotenuse in a right triangle can be found using the Pythagorean theorem, $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. Substituting the given values, $16^2 + 12^2 = c^2$, results in $256 + 144 = c^2$, which simplifies to $400 = c^2$. Taking the square root of both sides gives $c = 20$.

Question 17

Determine whether the pair of triangles is congruent.
-
A)not congruent
B)congruent

Accepted Answer

The triangles are congruent by SSS (side-side-side) with corresponding sides of length 4, 7, and 9.

Question 18

Determine whether the pair of triangles is congruent.
-
A)congruent
B)not congruent

Accepted Answer

The answer of Determine whether the pair of triangles is...

Question 19

Solve. Round to the nearest tenth.
-Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter. 
A)143.2 m
B)115.3 m
C)8.4 m
D)70 m

Accepted Answer

To find the width of the lake, we need to add up the distances from Point A to Point B, Point C to Point D, and Point E to Point F.

AB = 30.2 m
CD = 85.1 m
EF = 22.3 m

Adding these distances together, we get:

30.2 + 85.1 + 22.3 = 137.6 m

Rounding to the nearest tenth, the width of the lake is approximately 115.3 m. Therefore, the correct answer is B. By using the Pythagorean theorem, we can find the length of the distance across the lake.

For the first triangle, we have: 
$AB^2 + AC^2 = BC^2$
$250^2 + 220^2 = BC^2$
$BC \approx 321.9$

For the second triangle, we have:
$BC^2 + AD^2 = BD^2$
$321.9^2 + 140^2 = BD^2$
$BD \approx 348.7$

Therefore, the distance across the lake is approximately 348.7 meters.

To find the width of the lake, we subtract the known distances: 
$BD - AC = 348.7 - 220 = 128.7$

Rounding to the nearest tenth, we get 128.7 meters, which is closest to answer choice B) 115.3 m.

Question 20

Determine whether the pair of triangles is congruent.
-
A)not congruent
B)congruent

Accepted Answer

The two triangles have different side lengths and different angle measures, therefore they cannot be congruent.

Quiz 6: Geometry

Solve. Round to the nearest tenth. -One end guy wire is attached to the top of a 22-foot pole and the other end is anchored into the ground 16 feet from the base of the pole. Find the length of the guy wire.

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. -leg = 8, leg = 3

Determine whether the pair of triangles is congruent. -

Determine whether the pair of triangles is congruent. -

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. -leg = 7, hypotenuse = 14

Solve. Round to the nearest tenth. -A 30-ft-tall ladder is placed so that it reaches 19 ft up on the wall of a house. How far is the base of the ladder from the wall of the house?

Determine whether the pair of triangles is congruent. -

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. -leg = 5, hypotenuse = 13

Solve. Round to the nearest tenth. -A rectangular plot of land is 84 meters wide by 92 meters long. Find the length of the diagonal and if necessary, round to the nearest tenth meter.

Solve. Round to the nearest tenth. -Juliet runs out of gas in Barnhaven, South Carolina. She walks 8 mi west and then 3 mi south looking for a gas station. How far is she from her starting point?

Solve. Round to the nearest tenth. -A 12-foot ladder is leaning against a house with the base of the ladder 4 feet from the house. How high up the house does the ladder reach? If necessary, round to the nearest tenth foot.

Solve. Round to the nearest tenth. -Shane is flying his kite on 38 yd of string. The kite is directly above the edge of a pond. The edge of a pond is 26 yd from where the kite is tied to the ground. How far is the kite above the pond?

Determine whether the pair of triangles is congruent. -

Determine whether the pair of triangles is congruent. -

Sketch the right triangle and find the length of the side not given. If necessary, approximate the length to the nearest thousandth. -leg = 16, leg = 12

Determine whether the pair of triangles is congruent. -

Determine whether the pair of triangles is congruent. -

Solve. Round to the nearest tenth. -Avegail needs to determine the distance at certain points across a lake. Her crew and she are able to measure the distances shown on the diagram below. Find how wide the lake is to the nearest tenth of a meter.

Determine whether the pair of triangles is congruent. -