# Worksheet: The Sine Ratio

In this worksheet, we will practice finding angles and sides in a right triangle using the sine ratio.

**Q1: **

Find giving the answer to the nearest second.

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**Q2: **

Find , given is a right triangle at where and .

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**Q3: **

Find the measure of , given is an isosceles trapezoid where and giving the answer to the nearest second.

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**Q5: **

In the given figure, and . What is?

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**Q6: **

Find , given that is a right triangle at , where the point lies on , is perpendicular to , , and .

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**Q7: **

The distance between two villages and is 13 km where is west of . Village is located east of north of and north of west of . Find the distance between and giving the answer to the nearest kilometer.

**Q8: **

, , and are three towns that lie in the same horizontal plane. lies 38 km southwest of . lies east of north of and lies east of north of . Find the length of giving the answer to the nearest kilometer.

**Q9: **

In the given figure, and . What is ?

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- E

**Q10: **

is a right-angled triangle at where and . Find the length of giving the answer to two decimal places.

**Q11: **

Find the value of given is a right-angled triangle at , , and .

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- D

**Q12: **

In the given figure, , , and . Work out the height of the triangle to 2 decimal places.

**Q13: **

In the given figure, , , and . Work out the height of the triangle to 2 decimal places.

**Q14: **

A mountain has a uniform incline of . If a person walks 127 meters to the peak of the mountain, how tall is the mountain? Give the answer to the nearest meter.

**Q15: **

What is the value of in the given triangle?

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**Q16: **

A circle has a radius of 16 cm. A chord is drawn where the central angle is . Find the length of the chord giving the answer to three decimal places.

**Q17: **

Consider the following right triangle .

Which of the following statements is true?

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- E

Find the value of (usually written as: ).

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**Q18: **

In the given figure, has been extended to the point such that and are perpendicular. Work out the length of to two decimal places.

**Q19: **

What is the value of in the given triangle?

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**Q20: **

Find given is an isosceles trapezoid where and . Give the answer to the nearest second.

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- D

**Q21: **

A ladder 3 meters long leans against a wall. Find the vertical height of the ladder, given that the angle between the ladder and the ground is .

- A m
- B m
- C m
- D m

**Q22: **

is a right-angled triangle at where and . Find the lengths , , and the angle in radian, giving the answers to three decimal places.

- A, ,
- B, ,
- C, ,
- D, ,

**Q23: **

is an isosceles trapezoid where , , , and . Find and giving the answer to the nearest second.

- A,
- B,
- C,
- D,

**Q24: **

For the given figure, , , and . Work out the measure of . Give your answer to two decimal places.

**Q25: **

The positions of three towns are shown in the diagram. Towns and are 130 km apart. Find the distance between towns and and the distance between towns and . Give your answers to the nearest kilometer.

- A,
- B,
- C,
- D,