# Lesson Worksheet: The Cosine Ratio Mathematics

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:

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

• A
• B
• C
• D
• E

Q24:

A ladder is leaning against a vertical wall where the angle of inclination with the ground is . The lower end of the ladder moves metres away from the wall and the angle of inclination becomes . Find the length of the ladder giving the answer to one decimal place.

Q25:

Find given is an isosceles triangle where and . Give the answer to the nearest second. • A
• B
• C
• D