Question 1

Find A if C = 4 and B = 2. Round answer to the nearest thousandth.

Accepted Answer

The answer of Find A if C = 4 and...

Question 2

Find the number of degrees of each angle of a regular decagon (10 sides).

Accepted Answer

In a regular decagon, the sum of all the interior angles is given by:
Sum of interior angles = (n-2) × 180°, where n is the number of sides.
Substituting n=10, we get: 
Sum of interior angles = (10-2) × 180° = 8 × 180° = 1440°.
Since all the angles in a regular polygon are congruent, we can divide the sum by the number of angles to find the measure of each angle:
Measure of each angle = Sum of interior angles / Number of angles
Measure of each angle = 1440° / 10 = 144°.

Therefore, the answer is choice C (144°).

Question 3

Determine BC if AC = 4.71 ft and AB = 10.28 ft. Round to the nearest hundredth.

Accepted Answer

The answer of Determine BC if AC = 4.71 ft...

Question 4

Find the number of degrees in each angle of a regular octagon.

Accepted Answer

The sum of the interior angles of an n-sided polygon is given by the formula (n-2)×180°. For an octagon (n=8), this sum is (8-2)×180° = 6×180° = 1080°. Since a regular octagon has all angles equal, each angle is 1080°/8 = 135°.

Question 5

A ladder is leaning against the wall of a house with the bottom of the ladder 5 feet from the wall. The top of the ladder extends 12 feet up the wall. How long is the ladder?

Accepted Answer

The answer of A ladder is leaning against the wall...

Question 6

Find the hypotenuse of a right triangle whose legs measure 5 and 12 m.

Accepted Answer

The answer of Find the hypotenuse of a right triangle...

Question 7

A cannery processes green beans. One of the pieces of equipment it uses is called a sniper because it snips off the ends of the green beans. Inside the 6-foot drum is a series of triangular shaped blades, 3 in. on a side, connected in a row the length of the drum. What is the area covered by the blades inside the sniper drum?

Accepted Answer

The answer of A cannery processes green beans. One of...

Question 8

A conduit ABCD must be made so that zCBE is 45°. If BE = 5 cm and AK = 16 cm, find the length of the conduit to the nearest thousandth of a centimeter.

Accepted Answer

The answer of A conduit ABCD must be made so...

Question 9

What is the measurement needed of the third side of a triangle with two sides of 10 mm and 10 mm to make it a 45°, 45°, 90° triangle?

Accepted Answer

In a 45°, 45°, 90° triangle, the ratio of the sides is x:x:x√2 (where x is the length of the two equal sides).
So, in this case, the third side would be 10√2 mm or approximately 14.14 mm (since the two equal sides are already 10 mm each). Therefore, the best choice is B.

Question 10

The rafters of a house make a 30° angle with the joists. If the rafters have a 20-in. overhang and the center of the roof is 12 ft above the joists, how long must the rafters be cut?

Accepted Answer

The answer of The rafters of a house make a...

Question 11

A piece of round steel is milled to a point at one end. The angle formed by the point is the angle of taper. If the steel has a 22-mm diameter and a 60° angle of taper, find the length c of the taper.

Accepted Answer

The answer of A piece of round steel is milled...

Question 12

Given a 30°, 60°, 90° triangle, find the side opposite the 60º if the hypotenuse is 22.4 m.

Accepted Answer

In a 30°-60°-90° triangle, the side opposite the 60° angle is √3/2 times the hypotenuse. So, 22.4 * √3/2 ≈ 19.4 m.

Question 13

A 10-ft length of drainpipe has a cross-section as indicated below. What volume of water would the pipe hold?

Accepted Answer

We can use the formula for the volume of a cylinder to find the volume of water the pipe can hold. The radius of the pipe is given as 2 inches (since the diameter is 4 inches), and the length is given as 10 feet, or 120 inches. Therefore:

$V = \pi r^2 h = \pi (2^2)(120) = 960\pi \approx 3016.8$

Since the answer options are in cubic inches, we convert 3016.8 cubic inches to the nearest whole number, which is 3017 cubic inches. That is equivalent to answer option B, which is the correct answer.

Question 14

Find the total length to the nearest inch of the conduit ABCD if XY = 6 ft, CE =14 in., and zCBE = 30°

Accepted Answer

The answer of Find the total length to the nearest...

Question 15

A V-slot forms a triangle whose angle at the vertex is 60°. The depth of the slot is 24 mm. Find the width of the V-slot.

Accepted Answer

The answer of A V-slot forms a triangle whose angle...

Question 16

Find the length of the wire attached to a light pole 2.5 feet from the top of the light pole. The pole is 36 feet high. The wire is secured with a two-foot screw anchor 18 feet from the
Base of the pole.

Accepted Answer

The answer of Find the length of the wire attached...

Question 17

Determine AB if AC = 123.4 m and BC = 87.6 m. Round to the nearest tenth.

Accepted Answer

We can use the Pythagorean theorem to solve for AB: AB = √(AC² - BC²) = √(123.4² - 87.6²) = 151.3 m (rounded to the nearest tenth). Therefore, the answer is D.

Question 18

Given a 45°, 45°, 90° triangle, find the hypotenuse if a leg is 12.3 cm.

Accepted Answer

In a 45°, 45°, 90° triangle, the hypotenuse is equal to the length of one leg multiplied by the square root of 2. Therefore, the hypotenuse in this case is 12.3 cm multiplied by the square root of 2, which is approximately 17.39 cm.

Question 19

A manufacturer recommends attaching a guy wire to its 40-ft antenna at a 45° angle. If the antenna is installed on a flat surface, how long must the guy wire be (to the nearest foot)if it is attached to the antenna 4 ft from the top.

Accepted Answer

The guy wire forms the hypotenuse of a right triangle with legs of length 40 ft and 4 ft. The Pythagorean Theorem gives the length of the guy wire as sqrt(40^2 + 4^2) = sqrt(1600 + 16) = sqrt(1616) = 40.2 ft. To the nearest foot, the length of the guy wire is 40 ft.

Question 20

What is the measurement needed of the third side of a triangle with two sides of 7 m and 14 m to make it a 30°, 60°, 90° triangle?

Accepted Answer

In a 30°, 60°, 90° triangle, the ratio of the sides is 1:√3:2. 
So, if the shorter leg (opposite the 30° angle) is 7 m, the longer leg (opposite the 60° angle) will be 7√3 m (7 times the square root of 3). 
To find the length of the hypotenuse (opposite the 90° angle), we multiply the length of the shorter leg by 2, which gives us 14 m.
Therefore, if we subtract the square of the shorter leg from the square of the longer leg and take the square root of the result, we get the length of the missing side. 
c = √(14^2 - 7^2) 
c = √147 
c = 12.12 m 
Thus, the answer is C.

Quiz 18: Triangles