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In this lesson, we will learn how to find the value of a missing side length in a right triangle by choosing the appropriate trigonometric ratio for a given angle.

Q1:

Find the length of π΅ πΆ giving the answer to two decimal places.

Q2:

Find π₯ to two decimal places.

Q3:

Q4:

Given the following figure, find the lengths of π΄ πΆ and π΅ πΆ and the measure of β π΄ π΅ πΆ in degrees. Give your answers to two decimal places.

Q5:

A 23 ft ladder leans against a building such that the angle between the ground and the ladder is 8 0 β . How high does the ladder reach up the side of the building?

Q6:

A kite, which is at a perpendicular height of 44 m, is attached to a string inclined at 6 0 β to the horizontal. Find the length of the string accurate to one decimal place.

Q7:

Find the length of π΄ πΆ , given that π΄ π΅ = 1 9 c m , π· πΈ = 1 1 c m , and πΆ πΈ = 2 1 c m .

Q8:

A person observes a point on the ground from the top of a hill that is 1.56 km high. The angle of depression is 2 9 β . Find the distance between the point and the observer giving the answer to the nearest metre.

Q9:

π΄ π΅ πΆ is an isosceles triangle where π΄ π΅ = π΄ πΆ = 9 c m , π΄ π· β π΅ πΆ and π β πΆ = 3 4 β . Find the length of π΅ πΆ giving the answer to one decimal place.

Q10:

In the given figure, find π₯ . Give your answer to two decimal places.

Q11:

Find the length of π΄ πΆ given π΄ π΅ πΆ is a right-angled triangle at π΅ where s i n πΆ = 9 1 6 and π΄ π΅ = 1 8 c m .

Q12:

A builder leans a 6-foot plank of wood against a vertical wall. If one end of the plank is 1.5 feet from the bottom of the wall, what is the angle between the plank and the wall?

Q13:

A kite has a string of length 75 metres. The angle the string makes with the horizontal ground is 5 3 β . Find the height of the kite from the ground giving the answer to two decimal places.

Q14:

The angle of elevation between an aeroplane 10βββ000 m high and a person on a point on the ground is 3 8 6 β² β . Find the distance between the point and the aeroplane giving the answer to the nearest metre.

Q15:

π΄ π΅ πΆ is a triangle where π΄ πΆ = 3 4 c m , π΅ πΆ = 4 0 c m , and π β πΆ = 4 6 β . Point π· lies on πΆ π΅ where π΄ π· β π΅ πΆ . Find the height of the triangle drawn from point π΅ to β ο© ο© ο© ο© β π΄ πΆ giving the answer to two decimal places.

Q16:

π΄ π΅ πΆ π· is a rectangle where π΄ πΆ = 4 9 . 6 c m and π β π΄ πΆ π΅ = 2 6 5 4 β² β . Find the lengths of π΄ π΅ and π΅ πΆ giving the answer to three decimal places.

Q17:

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