Sec 2 Mathematics Trigonometric Ratios topical questions

Relative to angle θ in a right triangle, the opposite side is 5, the adjacent side is 12 and the hypotenuse is 13.

1. (a)Write tan θ as a fraction.[1]
2. (b)Write sin θ as a fraction.[1]
3. (c)Write cos θ as a fraction.[1]

Relative to angle θ, a right triangle has opposite side 8, adjacent side 15 and hypotenuse 17.

1. (a)Write sin θ as a fraction.[1]
2. (b)Write cos θ as a fraction.[1]
3. (c)Write tan θ as a fraction.[1]

Use a calculator to evaluate each ratio.

1. (a)tan 45°[1]
2. (b)sin 30°[1]
3. (c)cos 60°[1]

Relative to angle θ in a right triangle, the opposite side is 6, the adjacent side is 8 and the hypotenuse is 10.

1. (a)Write tan θ as a fraction in its simplest form.[1]
2. (b)Write sin θ as a fraction in its simplest form.[1]
3. (c)Write cos θ as a fraction in its simplest form.[1]

Evaluate each ratio (calculator in degree mode).

1. (a)sin 90°[1]
2. (b)tan 0°[1]
3. (c)cos 0°[1]

Find the unknown side in each right triangle, correct to 1 decimal place.

1. (a)Hypotenuse 10, angle 40°, find the opposite side.[2]
2. (b)Adjacent side 6, angle 55°, find the hypotenuse.[2]

In a right triangle, an angle of 35° has an opposite side of 8.

1. (a)Which ratio links the angle, the opposite side and the adjacent side?[1]
2. (b)Find the adjacent side, correct to 1 decimal place.[2]
3. (c)Explain why the sine ratio cannot be used with the information given.[1]

In a right triangle, the side opposite θ is 9 and the adjacent side is 12.

1. (a)Write the ratio for tan θ.[1]
2. (b)Find θ, correct to 1 decimal place.[2]
3. (c)Is θ larger or smaller than 45°? Give a quick reason.[1]

A 6 m ladder leans against a wall at 70° to the horizontal ground.

1. (a)How high up the wall does the ladder reach? (1 decimal place)[2]
2. (b)How far is the ladder’s foot from the wall? (1 decimal place)[2]

Find the unknown side in each right triangle, correct to 1 decimal place.

1. (a)Opposite side 11, angle 42°, find the adjacent side.[2]
2. (b)Hypotenuse 26, angle 35°, find the opposite side.[2]

A flagpole casts a 12 m shadow when the sun makes 55° with the ground.

1. (a)Find the height of the flagpole, correct to 1 decimal place.[2]
2. (b)At the same moment a 2 m stick casts a shadow. Find the shadow’s length, correct to 2 decimal places.[2]

A wheelchair ramp guideline says the ramp may make at most 4.8° with the ground.

1. (a)Which ratio links the angle, the rise (opposite) and the horizontal run (adjacent)?[1]
2. (b)Find the greatest rise allowed over a 10 m run, correct to 2 decimal places.[2]
3. (c)A proposed ramp rises 0.5 m over a 12 m run. Find its angle and say whether it passes.[2]

A roof has two identical rafters, each 5 m long, rising at 35° to the horizontal and meeting at the peak.

1. (a)Find the height of the peak above the ceiling line, correct to 2 decimal places.[2]
2. (b)Find the total horizontal span covered by the two rafters, correct to 2 decimal places.[2]
3. (c)Explain why each rafter acts as the hypotenuse of its triangle.[1]

At a certain hour, a pole casts a 7 m shadow, and the sun’s rays make 52° with the ground.

1. (a)Find the pole’s height, correct to 2 decimal places.[2]
2. (b)A second pole casts a 4 m shadow at the same moment. Find its height, correct to 2 decimal places.[2]
3. (c)Explain why the same angle works for both poles.[1]

A zipline runs from the top of a 20 m tower to an anchor on the ground 60 m from the tower’s base.

1. (a)Find the angle the zipline makes with the ground, correct to 1 decimal place.[2]
2. (b)Find the length of the zipline, correct to 1 decimal place.[2]
3. (c)Name the two tools used in (a) and (b) and say why each was needed.[1]