# 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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- D

**Q2: **

Find , given is a right-angled triangle at where and .

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- D

**Q3: **

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

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**Q6: **

In the given figure, has been extended to the point such that and are perpendicular.

Work out the value of to 4 decimal places.

Work out the value of to 4 decimal places.

Work out the length of to 2 decimal places.

Work out the area of the triangle to 2 decimal places.

**Q7: **

In the given figure, and . What is?

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- E

**Q8: **

In the given figure, , , and .

Calculate the height to 2 decimal places.

Calculate the area of the triangle to 2 decimal places.

**Q9: **

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

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**Q11: **

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 kilometre.

**Q14: **

, , 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 kilometre.

**Q15: **

In the given figure, and . What is ?

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- E

**Q16: **

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

**Q17: **

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

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**Q18: **

In the given figure, , , and .

Calculate the height to 2 decimal places.

Calculate the area of the triangle to 2 decimal places.

**Q19: **

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

**Q20: **

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

**Q21: **

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.

- A 60 m
- B 239 m
- C 271 m
- D 68 m
- E 112 m

**Q22: **

What is the value of in the given triangle?

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**Q23: **

Find the area of the triangle given and . Give the answer to two decimal places.

- A
210 cm
^{2} - B
184.66 cm
^{2} - C
100 cm
^{2} - D
369.32 cm
^{2}

**Q24: **

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.

**Q25: **

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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