Trigonometry for Carpenters: Master Angles and Measurements

Question 1

What is the value of the tangent of 30°?

Accepted Answer

0.5

Answer

0.7

Answer

1

Answer

√3

Question 2

A roof has a pitch of 4/12. What is the angle of the roof to the nearest degree?

Accepted Answer

27°

Answer

16°

Answer

34°

Answer

45°

Question 3

Which of the following is NOT a trigonometric function?

Accepted Answer

Quadratic

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 4

What is the reciprocal of the cosine function?

Accepted Answer

Secant

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 5

What is the value of sin(90°)?

Accepted Answer

1

Answer

0

Answer

√2

Answer

Undefined

Question 6

Which trigonometric function represents the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 7

What is the formula for calculating the pitch of a roof given the angle of inclination?

Accepted Answer

Pitch = Angle of Inclination / 12

Answer

Pitch = Angle of Inclination

Answer

Pitch = 12 / Angle of Inclination

Answer

Pitch = 1 / Angle of Inclination

Question 8

Which trigonometric function is used to determine the angle of a stair stringer?

Accepted Answer

Tangent

Answer

Sine

Answer

Cosine

Answer

Cotangent

Question 9

What is the difference between the sine and cosine functions?

Accepted Answer

Sine measures the ratio of the opposite side to the hypotenuse, while cosine measures the ratio of the adjacent side to the hypotenuse.

Answer

Cosine measures the ratio of the opposite side to the hypotenuse, while sine measures the ratio of the adjacent side to the hypotenuse.

Answer

Sine and cosine are the same function.

Answer

Sine measures the angle of an angle, while cosine measures the length of a side.

Question 10

What is the formula for calculating the area of a triangle?

Accepted Answer

Area = 1/2 * Base * Height

Answer

Area = Base * Height

Answer

Area = 1/4 * Base * Height

Answer

Area = 2 * Base * Height

Question 11

A staircase has a rise of 7 inches and a run of 10 inches. What is the angle of the staircase?

Accepted Answer

38.66 degrees

Answer

35.82 degrees

Answer

42.86 degrees

Answer

45 degrees

Question 12

Which trigonometric function is used to calculate the length of the adjacent side of a right triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 13

A ladder is leaning against a wall. The ladder is 12 feet long and the base of the ladder is 9 feet from the wall. What is the angle between the ladder and the wall?

Accepted Answer

40.89 degrees

Answer

36.87 degrees

Answer

45 degrees

Answer

53.13 degrees

Question 14

What is the unit of measurement for angles when working in degrees?

Accepted Answer

Degrees

Answer

Radians

Answer

Gradians

Answer

Mils

Question 15

Which trigonometric function is used to calculate the length of the hypotenuse of a right triangle?

Accepted Answer

Secant

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 16

In a right triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. If the sine of an angle is 0.5, what is the measure of the angle?

Accepted Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Answer

90 degrees

Question 17

Convert the angle 3π/4 radians to degrees.

Accepted Answer

135°

Answer

120°

Answer

90°

Answer

45°

Question 18

Which of the following is the inverse function of sine?

Accepted Answer

Arcsine

Answer

Arccosine

Answer

Cotangent

Question 19

When using a protractor to measure an angle, the reading should be taken from:

Accepted Answer

The zero mark on the protractor

Answer

The center of the protractor

Answer

The outer edge of the protractor

Question 20

To find the cosine of an angle, which of the following adjacent side and hypotenuse side lengths is required?

Accepted Answer

Adjacent side and hypotenuse side

Answer

Adjacent side and opposite side

Answer

Opposite side and hypotenuse side

Question 21

What is the range of values for the sine function?

Accepted Answer

[-1, 1]

Answer

[0, 1]

Answer

[-∞, ∞]

Question 22

A flagpole casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the flagpole is 30 degrees, what is the height of the flagpole?

Accepted Answer

25.98 feet

Answer

30 feet

Answer

45 feet

Question 23

Calculate the angle of inclination for a roof with a pitch of 6/12.

Accepted Answer

26.5 degrees

Answer

30 degrees

Answer

45 degrees

Answer

60 degrees

Question 24

Convert the angle 45 degrees into radians. Express your answer as a fraction of π.

Accepted Answer

π/4

Answer

π/2

Answer

2π/3

Answer

3π/4

Question 25

To determine the height of a wall, you measure its shadow as 12 feet long, and the angle of elevation from the tip of the shadow to the top of the wall is 30 degrees. What is the height of the wall?

Accepted Answer

10 feet

Answer

6 feet

Answer

12 feet

Answer

18 feet

Question 26

A circular saw blade has a 10-inch diameter. What is the angle formed by two radii drawn to the endpoints of an arc that measures 3 inches along the blade's circumference?

Accepted Answer

34.38 degrees

Answer

17.19 degrees

Answer

51.57 degrees

Answer

68.76 degrees

Question 27

A carpenter is cutting a molding with a miter saw. The miter cut should be 45 degrees. What is the setting on the saw that will produce this angle?

Accepted Answer

45 degrees

Answer

22.5 degrees

Answer

67.5 degrees

Answer

90 degrees

Question 28

A rectangular room is 12 feet long and 8 feet wide. What is the diagonal length of the room?

Accepted Answer

14.42 feet

Answer

16 feet

Answer

18 feet

Answer

20 feet

Question 29

In a right triangle, what is the trigonometric function cosine used to calculate?

Accepted Answer

The ratio of the length of the adjacent side to the length of the hypotenuse

Answer

The ratio of the length of the opposite side to the length of the hypotenuse

Answer

The ratio of the length of the hypotenuse to the length of the adjacent side

Question 30

What is the value of sin(30°)?

Accepted Answer

0.707

Answer

0.5

Answer

1.0

Answer

1.414

Question 31

A staircase has 12 steps, each with a rise of 8 inches. What is the angle of the staircase?

Accepted Answer

48°

Answer

30°

Answer

36°

Answer

42°

Question 32

In a right triangle, what is the tangent of a 30-degree angle?

Accepted Answer

0.5

Answer

0

Answer

1

Question 33

A roof has a pitch of 6:12. What is the angle of elevation of the roof?

Accepted Answer

26.5°

Answer

30°

Answer

45°

Answer

60°

Question 34

A roof has a pitch of 6/12. What is the angle of elevation from the horizontal to the roof line?

Accepted Answer

26.57°

Answer

60°

Answer

45°

Answer

30°

Question 35

A stair has a rise of 8 inches and a run of 12 inches. What is the angle of inclination of the stair?

Accepted Answer

34.29°

Answer

75°

Answer

60°

Answer

45°

Question 36

A saw blade has a diameter of 10 inches and cuts a groove that is 1 inch deep. What is the angle formed by the blade and the surface of the wood?

Accepted Answer

5.71°

Answer

10°

Answer

15°

Answer

20°

Question 37

Which trigonometric function is used to find the length of the side opposite to a given angle in a right triangle?

Accepted Answer

Sine

Answer

Tangent

Answer

Cosine

Question 38

A ladder is leaning against a wall and makes an angle of 75 degrees with the ground. If the ladder is 10 feet long, how far up the wall does it reach?

Accepted Answer

9.66 feet

Answer

10 feet

Answer

8 feet

Answer

12 feet

Question 39

A rectangular deck has a length of 12 feet and a width of 8 feet. What is the length of the diagonal of the deck?

Accepted Answer

14.42 feet

Answer

18 feet

Answer

10 feet

Answer

16 feet

Question 40

A ramp has a slope of 1:12. What is the angle of inclination of the ramp?

Accepted Answer

4.76°

Answer

15°

Answer

20°

Answer

10°

Question 41

Which of the following is NOT a trigonometric function?

Accepted Answer

Pythagorean Theorem

Answer

Cosine

Answer

Sine

Answer

Tangent

Question 42

A roof has a pitch of 6:12. What is the angle of the roof?

Accepted Answer

26.57°

Answer

36.87°

Answer

45°

Answer

12.67°

Question 43

A stair has a rise of 7 inches and a run of 10 inches. What is the angle of the stair?

Accepted Answer

35.06°

Answer

45°

Answer

60°

Answer

26.57°

Question 44

A rectangular piece of plywood is 4 feet wide and 8 feet long. What is the length of the diagonal?

Accepted Answer

8.94 feet

Answer

16 feet

Answer

6.93 feet

Answer

12 feet

Question 45

What is the cosine of a 45° angle?

Accepted Answer

0.707

Answer

1

Answer

0.5

Answer

1.414

Question 46

A carpenter wants to build a roof with a pitch of 4/12. What is the angle of the roof, rounded to the nearest degree?

Accepted Answer

18.43°

Answer

30°

Answer

45°

Answer

60°

Question 47

A carpenter is using a ladder that is 15 feet long. If the base of the ladder is 5 feet away from the wall, how high up the wall will the ladder reach?

Accepted Answer

14.42 feet

Answer

16 feet

Answer

12 feet

Answer

8 feet

Question 48

A carpenter is building a rectangular deck with a diagonal brace. The deck is 10 feet long and 8 feet wide. What is the length of the diagonal brace?

Accepted Answer

12.81 feet

Answer

10 feet

Answer

18 feet

Answer

20 feet

Question 49

A carpenter is building a ramp with a slope of 1:8. What is the angle of the ramp, rounded to the nearest degree?

Accepted Answer

7.13°

Answer

20°

Answer

10°

Answer

15°

Question 50

A carpenter is building a roof truss with a span of 20 feet. If the rise of the truss is 6 feet, what is the length of the rafter?

Accepted Answer

11.31 feet

Answer

4 feet

Answer

16 feet

Answer

20 feet