# Worksheet: The Sine Ratio

In this worksheet, we will practice finding angles and sides in a right triangle using the sine ratio.

Q1:

Find giving the answer to the nearest second. • A
• B
• C
• D

Q2:

Find , given is a right triangle at where and . • A
• B
• C
• D

Q3:

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

Q4:

Find the value of giving the answer in radians to two decimal places. Q5:

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

Q6:

Find , given that is a right triangle at , where the point lies on , is perpendicular to , , and . • A
• B
• C
• D

Q7:

The distance between two villages and is 13 km where is west of . Village is located east of north of and north of west of . Find the distance between and giving the answer to the nearest kilometer.

Q8:

, , and are three towns that lie in the same horizontal plane. lies 38 km southwest of . lies east of north of and lies east of north of . Find the length of giving the answer to the nearest kilometer.

Q9:

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

Q10:

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

Q11:

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

• A
• B
• C
• D

Q12:

In the given figure, , , and . Work out the height of the triangle to 2 decimal places. Q13:

In the given figure, , , and . Work out the height of the triangle to 2 decimal places. Q14:

A mountain has a uniform incline of . If a person walks 127 meters to the peak of the mountain, how tall is the mountain? Give the answer to the nearest meter.

Q15:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q16:

A circle has a radius of 16 cm. A chord is drawn where the central angle is . Find the length of the chord giving the answer to three decimal places.

Q17:

Consider the following right triangle . Which of the following statements is true?

• A
• B
• C
• D
• E

Find the value of (usually written as: ).

• A
• B
• C
• D
• E

Q18:

In the given figure, has been extended to the point such that and are perpendicular. Work out the length of to two decimal places. Q19:

What is the value of in the given triangle? • A
• B
• C
• D
• E

Q20:

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

Q21:

A ladder 3 meters long leans against a wall. Find the vertical height of the ladder, given that the angle between the ladder and the ground is .

• A m
• B m
• C m
• D m

Q22:

is a right-angled triangle at where and . Find the lengths , , and the angle in radian, giving the answers to three decimal places.

• A, ,
• B, ,
• C, ,
• D, ,

Q23:

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

Q24:

For the given figure, , , and . Work out the measure of . Give your answer to two decimal places. Q25:

The positions of three towns are shown in the diagram. Towns and are 130 km apart. Find the distance between towns and and the distance between towns and . Give your answers to the nearest kilometer. • A,
• B,
• C,
• D,