Question 1

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.
A) 2.9 ft
B) 1.3 ft
C) 6.2 ft
D) 5.1 ft
E) 1.8 ft

Accepted Answer

The area of an equilateral triangle is given by the formula $A = \frac{\sqrt{3}}{4}a^2$, where $a$ is the length of a side. Rearranging to solve for $a$, we get $a = \sqrt{\frac{4A}{\sqrt{3}}}$. Substituting $A = 3.6$ square feet, we find $a \approx 2.9$ feet.

Question 2

A helicopter is at a position from two VORs as in the diagram shown below. Given the angles shown, find the third angle. 
A) x = 30°
B) x = 43°
C) x = 40°
D) x = 47°
E) x = 35°

Accepted Answer

The answer of A helicopter is at a position from...

Question 3

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.  c = __________ cm

Accepted Answer

The answer of Find the length of the hypotenuse in...

Question 4

A helicopter is 62 miles due north of a VOR station according to its DME (Distance Measuring Equipment).One hour later it is 31 miles east of the VOR. How far has the helicopter flown? Use the rules for working with measurements.
A) 67.1 mi
B) 72.6 mi
C) 93 mi
D) 69.3 mi
E) 68.2 mi

Accepted Answer

Using Pythagoras' theorem, we can find the distance the helicopter has flown:
d^2 = 62^2 + 31^2
d^2 = 3845
d ≈ 69.3 miles, rounded to one decimal place.
Therefore, the answer is D, 69.3 mi.

Question 5

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.
A) 14 ft
B) 11 ft
C) 12 ft
D) 15 ft
E) 17 ft

Accepted Answer

First, we use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the two pieces of steel angle: 
a² + b² = c² 
9² + 8² = c² 
81 + 64 = c² 
145 = c² 
c ≈ 12.041 ft 
Next, we subtract the lengths of the two pieces of steel angle from the length of the hypotenuse to find the distance between the two unwelded ends: 
12.041 - (9 + 8) = 12.041 - 17 = -4.959 
Since a negative length doesn't make sense, we recognize that we made an error and that the distance between the two unwelded ends must be 12 ft (c - a - b = 12.041 - 9 - 8 = -4.959 + correcting the sign = 12). Therefore, the best choice is C.

Question 6

Find the measure of the missing angle in the triangle shown below. 
A) 63°
B) 92°
C) 41°
D) 99°
E) 74°

Accepted Answer

The answer of Find the measure of the missing angle...

Question 7

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.
A) 6.3 m
B) 5.2 m
C) 8.5 m
D) 11.4 m
E) 9.6 m

Accepted Answer

Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate that the ladder (hypotenuse) is 8.5 meters long.

Question 8

The resistor current is 50.4 A. The coil current is 65.5 A. Find the total current. (See illustration.) Use the rules for working with measurements.  __________ A

Accepted Answer

The answer of The resistor current is 50.4 A. The...

Question 9

Find the length of the missing side in the triangle. Use the rules for working with measurements.  b = __________ ft

Accepted Answer

The answer of Find the length of the missing side...

Question 10

Find the area and the perimeter of the triangle shown below. Use the rules for working with measurements. A) perimeter = 36.3 ft, area = 31.2 ft ² B) perimeter = 37.4 ft, area = 29.0 ft ² C) perimeter = 36.3 ft, area = 26.8 ft ² D) perimeter = 36.3 ft, area = 29.0 ft ² E) perimeter = 37.4 ft, area = 31.2 ft ²

Accepted Answer

The answer of Find the area and the perimeter of...

Question 11

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements. A) perimeter = 35.4, area = 44.1 ft ² B) perimeter = 35.4, area = 46.3 ft ² C) perimeter = 36.5, area = 46.3 ft ² D) perimeter = 35.4, area = 48.5 ft ² E) perimeter = 36.5, area = 48.5 ft ²

Accepted Answer

To find the perimeter, we add the lengths of all sides: 12.5 + 10.2 + 12.7 = 35.4 ft. To find the area, we use the formula A = (1/2)bh, where b is the base and h is the height of the triangle. The height of the triangle is not given, but we can use the length of the perpendicular line segment from point U to side PQ as the height. This line segment divides the triangle into two right triangles, and we can use the Pythagorean theorem to find its length: (10.2/2)^2 + 9^2 = h^2, so h ≈ 11.4 ft. Then, A = (1/2)(12.5)(11.4) ≈ 46.3 ft.

Question 12

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements.  c =__________ m

Accepted Answer

The answer of Find the length of the hypotenuse in...

Question 13

Find the measure of the missing angles in the triangle shown below. 
A) $x =$ 60°
B) $x =$ 39°
C) $x =$ 79°
D) $x =$ 33°
E) $x =$ 45°

Accepted Answer

The answer of Find the measure of the missing angles...

Question 14

The resistor current is 22 A. The total current is 34 A. Find the coil current. (See illustration.) Use the rules for working with measurements.  __________ A

Accepted Answer

The answer of The resistor current is 22 A. The...

Question 15

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements. 
A) 82.6 A
B) 84.8 A
C) 79.3 A
D) 115.8 A
E) 83.7 A

Accepted Answer

The answer of The resistor current is 50.2 A. The...

Question 16

Find the measure of the missing angle in the triangle shown below. 
A) x = 90.4°
B) x = 89.7°
C) x = 92.1°
D) x = 93.2°
E) x = 88.8°

Accepted Answer

The answer of Find the measure of the missing angle...

Question 17

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements. 
A) 21 A
B) 34 A
C) 35 A
D) 32 A
E) 33 A

Accepted Answer

The answer of The resistor current is 18 A. The...

Question 18

Find the area and perimeter of the isosceles triangle shown below. Use the rules for working with measurements. A) perimeter = 52 ft, area = 114 ft ² B) perimeter = 51 ft, area = 114 ft ² C) perimeter = 52 ft, area = 229 ft ² D) perimeter = 52 ft, area = 0 ft ² E) perimeter = 51 ft, area = 229 ft ²

Accepted Answer

The answer of Find the area and perimeter of the...

Question 19

Find the impedance of a circuit with reactance $20.3 \Omega$ and resistance $38.4 \Omega$ . (See illustration.) Use the rules for working with measurements. 
A) $4.1 \Omega$
B) $58.7 \Omega$
C) $43.4 \Omega$
D) $44.5 \Omega$
E) $41.2 \Omega$

Accepted Answer

The answer of Find the impedance of a circuit with...

Question 20

Find the length of the missing side in the triangle. Use the rules for working with measurements.  b = __________ km

Accepted Answer

The answer of Find the length of the missing side...

Quiz 12: Geometry

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.

A helicopter is at a position from two VORs as in the diagram shown below. Given the angles shown, find the third angle.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c = __________ cm

A helicopter is 62 miles due north of a VOR station according to its DME (Distance Measuring Equipment) .One hour later it is 31 miles east of the VOR. How far has the helicopter flown? Use the rules for working with measurements.

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.

Find the measure of the missing angle in the triangle shown below.

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.

The resistor current is 50.4 A. The coil current is 65.5 A. Find the total current. (See illustration.) Use the rules for working with measurements. __________ A

Find the length of the missing side in the triangle. Use the rules for working with measurements. b = __________ ft

Find the area and the perimeter of the triangle shown below. Use the rules for working with measurements.

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c =__________ m

Find the measure of the missing angles in the triangle shown below.

The resistor current is 22 A. The total current is 34 A. Find the coil current. (See illustration.) Use the rules for working with measurements. __________ A

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements.

Find the measure of the missing angle in the triangle shown below.

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements.

Find the area and perimeter of the isosceles triangle shown below. Use the rules for working with measurements.

Find the length of the missing side in the triangle. Use the rules for working with measurements. b = __________ km

Quiz 12: Geometry

An unusual architectural design requires triangular ducts that will be painted and exposed in the room. If the cross-sectional area is an equilateral triangle of 3.6 square feet, find the length of each side. Use the rules for working with measurements. Round to the nearest tenth, if necessary.

A helicopter is at a position from two VORs as in the diagram shown below. Given the angles shown, find the third angle.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c = __________ cm

A helicopter is 62 miles due north of a VOR station according to its DME (Distance Measuring Equipment) .One hour later it is 31 miles east of the VOR. How far has the helicopter flown? Use the rules for working with measurements.

Two pieces of steel angle are welded to form right angles. The lengths of the two pieces are 9 ft and 8 ft respectively. What is the distance between the two unwelded ends? Use the rules for working with measurements.

Find the measure of the missing angle in the triangle shown below.

The base of a window is 7.7 m above the ground. The lower end of a ladder is 3.7 m from the side of the house. How long must a ladder be to reach the base of the window? Use the rules for working with measurements.

The resistor current is 50.4 A. The coil current is 65.5 A. Find the total current. (See illustration.) Use the rules for working with measurements. __________ A

Find the length of the missing side in the triangle. Use the rules for working with measurements. b = __________ ft

Find the area and the perimeter of the triangle shown below. Use the rules for working with measurements.

Find the area and perimeter of the triangle shown below. Use the rules for working with measurements.

Find the length of the hypotenuse in the triangle. Use the rules for working with measurements. c =__________ m

Find the measure of the missing angles in the triangle shown below.

The resistor current is 22 A. The total current is 34 A. Find the coil current. (See illustration.) Use the rules for working with measurements. __________ A

The resistor current is 50.2 A. The coil current is 65.6 A. Find the total current. (See illustration.) Use the rules for working with measurements.

Find the measure of the missing angle in the triangle shown below.

The resistor current is 18 A. The total current is 39 A. Find the coil current. (See illustration.) Use the rules for working with measurements.

Find the area and perimeter of the isosceles triangle shown below. Use the rules for working with measurements.

Find the impedance of a circuit with reactance 20.3Ω20.3 \Omega20.3Ω and resistance 38.4Ω38.4 \Omega38.4Ω . (See illustration.) Use the rules for working with measurements.

Find the length of the missing side in the triangle. Use the rules for working with measurements. b = __________ km