# Lesson Worksheet: Trigonometric Ratios of Special Triangles Mathematics • 11th Grade

In this worksheet, we will practice how to find the side lengths of 45-45-90 and 30-60-90 triangles using trigonometric ratios.

Q1:

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 m
• B4 m
• C m
• D m
• E m

Q2:

Find, in terms of , the length of the hypotenuse of this triangle.

• A
• B
• C
• D
• E

Q3:

Given that , find . Give an exact answer.

• A
• B
• C3
• D6
• E

Q4:

Find the ratio of the length of to the length of in its simplest form.

• A
• B
• C
• D
• E

Q5:

A flying kite is attached to a 90 m long string. Find the height of the kite if the angle between the string and the ground is .

• A m
• B45 m
• C m
• D180 m
• E m

Q6:

Find, in terms of , the length of the hypotenuse of the given triangle.

• A
• B
• C
• D
• E

Q7:

Given that , find . Give an exact answer.

• A cm
• B cm
• C cm
• D1 cm
• E4 cm

Q8:

Consider the rectangle in the following figure. If and the measure of , find the length of diagonal .

• A3 cm
• B cm
• C12 cm
• D cm
• E cm

Q9:

Given that , find the area of triangle .

• A cm2
• B cm2
• C cm2
• D cm2
• E1 cm2

Q10:

In the figure, the length of is .

Find the length of .

• A4
• B8
• C16
• D2
• E

Given that the length of is 6, find the length of . Give an exact answer.

• A
• B
• C
• D2
• E4