In this worksheet, we will practice identifying which trigonometric ratio to use to calculate sides and angles in right triangles.

**Q3: **

A chord is drawn in a circle whose radius is 8 cm. If the measure of its central angle is , calculate the length of the chord to the nearest thousandth.

**Q4: **

is a rhombus where the lengths of the diagonals and are 14.2 cm and 23.2 cm respectively. Find giving the answer to the nearest second.

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**Q5: **

From the top of a house 15 m tall, the angles of elevation and depression of the top and the base of a building are and respectively. Find the height of the building giving the answer to the nearest metre.

**Q6: **

is a triangle where , , and . Point lies on where . Find the area of giving the answer to two decimal places.

**Q7: **

Find the value of .

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**Q8: **

is a trapezium-shaped piece of land where is parallel to and . Find given that , , and . Give the answer to the nearest second.

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**Q9: **

The dimensions of a rectangular garden is 20 metres by 17 metres. Triangle represents the lawn where . Find giving the answer to the nearest second.

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**Q10: **

Find the lengths of and given is a right-angled triangle at where and . Give the answers to the nearest centimetre.

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**Q11: **

Two boys are on opposite sides of a tower. They see the top of the tower at angles of elevation and , respectively. If the height of the tower is 21 m, find the distance between the two boys to the nearest meter.

**Q12: **

In the given figure, , , and . Calculate the length of . Give your answer to two decimal places.

**Q13: **

is a right-angled triangle at , where and . Find the perimeter of , giving the answer to the nearest centimeter.

**Q14: **

is a triangle where , , and . Point lies on where . Find the area of giving the answer to two decimal places.