# Worksheet: Right Triangle Trigonometry: Solve for a Side

In this worksheet, we will practice finding 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 giving the answer to two decimal places. Q2:

Find to two decimal places. Q3:

Find to two decimal places. Q4:

Given the following figure, find the lengths of and and the measure of in degrees. Give your answers to two decimal places. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q5:

A 23 ft ladder leans against a building such that the angle between the ground and the ladder is . How high does the ladder reach up the side of the building? Give your answer to two decimal places.

Q6:

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

Q7:

Find the length of , given that , , and . • A cm
• B cm
• C cm
• D cm
• E cm

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 . Find the distance between the point and the observer giving the answer to the nearest meter.

Q9:

is an isosceles triangle where , and . Find the length of giving the answer to one decimal place. Q10:

Find the length of given is a right-angled triangle at where and .

Q11:

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

Q12:

is a triangle where , , and . Point lies on where . Find the height of the triangle drawn from point to giving the answer to two decimal places. Q13:

is a rectangle where and . Find the lengths of and giving the answer to three decimal places.

• A,
• B,
• C,
• D,

Q14:

Find the length of giving the answer to two decimal places. Q15:

In the given figure, , , and . Unless otherwise stated, give all solutions to the following questions to four decimal places. Work out the length of and .

• A2.8512, 7.1488
• B3.2184, 6.7816
• C1.7101, 8.2899
• D3.2899, 6.7101
• E4.6985, 5.3015

Using the Pythagorean theorem, or otherwise, calculate .

Q16:

Given the following figure, find and and the length of . Give your answers to two decimal places. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q17:

In the given figure, given that and , find the lengths of and and the measure of in degrees. Give your answers to two decimal places. • A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q18:

Find in the given figure. Give your answer to two decimal places. Q19:

Find given is a triangle where and .

Q20:

Find given is a right-angled triangle at where .

Q21:

Find the values of and giving the answer to three decimal places. • A,
• B,
• C,
• D,

Q22:

Find the values of and giving the answer to three decimal places. • A,
• B,
• C,
• D,

Q23:

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

• A
• B
• C
• D

Q24:

Find the value of , given that is a triangle, where , , and is drawn perpendicular to intersecting at .

• A
• B
• C
• D

Q25:

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

• A168
• B600
• C175
• D625