Worksheet: Applications of Trigonometric Ratios

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

Q1:

Find the area of triangle , given that , , and .

Q2:

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

• A6.20
• B5.20
• C8.00
• D9.54
• E10.55

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.

• A
• B
• C
• D
• E

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 .

• A
• B
• C
• D
• E

Q8:

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

• A
• B
• C
• D

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.

• A
• B
• C
• D

Q10:

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

• A ,
• B ,
• C ,
• D ,

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.

Q15:

Find the area of triangle , given that , , and .