# Worksheet: The Cosine Ratio

In this worksheet, we will practice finding missing lengths and angles in a triangle using the cosine ratios.

Q1:

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

Q4:

In the given figure, and . What is ? • A
• B
• C
• D
• E

Q5:

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. Q6:

Find the radius of circle given and . Give the answer to two decimal places. Q7:

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

Q8:

is a triangle, where , , and . Find the length of , giving your answer to the nearest centimeter.

Q9:

In the given figure, find the length of to two decimal places. Q10:

For the figure given, find to two decimal places. Q11: Q12:

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

Q13:

Find the length of giving the answer to two decimal places. Q14:

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

Q15:

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

Q16:

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. Q17:

Find the radius of circle given and . Give the answer to two decimal places. Q18:

is an isosceles trapezoid where and . Find and giving the answer to the nearest second. • A,
• B,
• C,
• D,

Q19:

In the given figure, where . What is the value of ? • A
• B
• C
• D
• E

Q20:

Find the value of . • A
• B
• C
• D

Q21:

In the given figure, the two triangles are similar. Work out the value of for . Give your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

Work out the value of for . Give your answer as a fraction in its simplest form.

• A
• B
• C
• D
• E

What can be said about the value of for two similar triangles?

• AThey are often equal.
• BThey are always equal.
• CThere is no relation.

Q22:

Find the value of . Q23:

A 20-feet ladder leans against the side of the building such that the bottom of the ladder is 4 feet from the bottom of the building. Health and safety specifications require the measure of the angle between the ladder and the ground to be between and . Does the ladder satisfy those specifications?

• Ano
• Byes

Q24:

is an isosceles triangle where and . Find the value of given lies on where .

• A
• B
• C
• D
• E

Q25:

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.