Worksheet: Finding Sides Using the Cosine Ratio

Practice finding a the hypotenuse and the adacent side using the cosine ratio. Questions on this worksheet involve right triangles or problems that lead to right triangles. Isosceles triangles and ladder problems are covered.

Q1:

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

Q2:

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

Q3:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

A 12.68 cm
B 59.31 cm
C 11.40 cm
D 28.93 cm
E 53.31 cm

Q4:

is a right triangle at where and . Find the length of giving the answer to two decimal places.

A 7.32 cm
B 34.22 cm
C 6.58 cm
D 16.69 cm
E 30.75 cm

Q5:

is a rectangle where the diagonal and . Find the length of giving the answer to two decimal places.

Q6:

is a rectangle where the diagonal and . Find the length of giving the answer to two decimal places.

Q7:

In the given figure, and . What is ?

Q8:

Find the radius of circle given and . Give the answer to two decimal places.

Q9:

Find the radius of circle given and . Give the answer to two decimal places.

Q10:

A swimming pool is in the shape of a trapezoid. Find the length of one of the equal sides giving the answer to one decimal place.

A 10.8 m
B 9.5 m
C 15.3 m
D 8.8 m
E 13.4 m

Q11:

A swimming pool is in the shape of a trapezoid. Find the length of one of the equal sides giving the answer to one decimal place.

A 7.2 m
B 5 m
C 10.4 m
D 8.8 m
E 9.2 m

Q12:

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

Q13:

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

Q14:

A student rests their 15 cm ruler against a pen pot such that it makes an angle of with the horizontal desk. How far is the bottom of the ruler from the bottom of the pot? Give your answer in centimeters to one decimal place.

Q15:

A ladder 8 meters long leans against a wall. Find the horizontal length between the base of the ladder and the wall given the angle between the ladder and the ground is .

A 4 m
B m
C m
D m
E m

Q16:

A ladder 2 meters long leans against a wall. Find the horizontal length between the base of the ladder and the wall given the angle between the ladder and the ground is .

A m
B m
C m
D 1 m
E m