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In this lesson, we will learn how to identify which trigonometric ratio to use to calculate sides and angles in right triangles.

Q1:

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

Q2:

Find the value of t a n π΄ .

Q3:

Two boys are on opposite sides of a tower. They see the top of the tower at angles of elevation 3 9 β and 2 6 β , respectively. If the height of the tower is 21 m, find the distance between the two boys to the nearest meter.

Q4:

π΄ π΅ πΆ π· is a trapezium-shaped piece of land where π΄ π· is parallel to π΅ πΆ and π΄ π΅ β π΅ πΆ . Find π β πΆ given that π΄ π· = 2 0 m , π΅ πΆ = 3 5 m , and π· πΆ = 2 5 m . Give the answer to the nearest second.

Q5:

π΄ π΅ πΆ is a right-angled triangle at π΅ , where π΄ π΅ = 2 6 c m and π β πΆ = 6 5 8 β² β . Find the perimeter of π΄ π΅ πΆ , giving the answer to the nearest centimeter.

Q6:

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 5 9 β and 4 4 β respectively. Find the height of the building giving the answer to the nearest metre.

Q7:

A chord is drawn in a circle whose radius is 8 cm. If the measure of its central angle is 1 0 0 β , calculate the length of the chord to the nearest thousandth.

Q8:

Q9:

π΄ π΅ πΆ is a triangle where π΄ πΆ = 3 5 c m , π΅ πΆ = 2 5 c m , and π β πΆ = 5 4 β . Point π· lies on πΆ π΅ where π΄ π· β π΅ πΆ . Find the area of π΄ π΅ πΆ giving the answer to two decimal places.

Q10:

π΄ π΅ πΆ is a triangle where π΄ πΆ = 3 8 c m , π΅ πΆ = 5 4 c m , and π β πΆ = 4 0 β . Point π· lies on πΆ π΅ where π΄ π· β π΅ πΆ . Find the area of π΄ π΅ πΆ giving the answer to two decimal places.

Q11:

Find the lengths of π΅ πΆ and π΄ πΆ given π΄ π΅ πΆ is a right-angled triangle at π΅ where π΄ π΅ = 1 5 c m and t a n πΆ = 3 4 . Give the answers to the nearest centimetre.

Q12:

The dimensions of a rectangular garden is 20 metres by 17 metres. Triangle π΄ πΈ πΆ represents the lawn where πΈ πΆ = 9 m . Find π β π΄ πΈ π΅ giving the answer to the nearest second.

Q13:

Find the area of triangle π΄ π΅ πΆ , given that π΄ π΅ = π΄ πΆ , π΅ πΆ = 2 0 c m , and c o s π΅ = 5 1 3 .

Q14:

Find the area of triangle π΄ π΅ πΆ , given that π΄ π΅ = π΄ πΆ , π΅ πΆ = 4 8 c m , and c o s π΅ = 4 5 .

Q15:

π΄ π΅ πΆ π· is a rhombus where the lengths of the diagonals π΄ πΆ and π΅ π· are 14.2 cm and 23.2 cm respectively. Find π β π΄ π· πΆ giving the answer to the nearest second.

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