# 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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**Q6: **

In the given figure, and . What is?

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**Q7: **

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

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**Q9: **

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.

**Q12: **

, , 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.

**Q13: **

In the given figure, and . What is ?

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**Q14: **

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

**Q15: **

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

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**Q16: **

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

**Q17: **

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

**Q18: **

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.

**Q19: **

What is the value of in the given triangle?

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**Q20: **

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.

**Q21: **

Consider the following right triangle .

Which of the following statements is true?

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Find the value of (usually written as: ).

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**Q22: **

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

**Q23: **

What is the value of in the given triangle?

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**Q25: **

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

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