# 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
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Q2:

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

Q3:

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

Q4:

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

A builder leans a 5-foot plank of wood against a vertical wall. If one end of the plank is 3 feet from the bottom of the wall, what is the angle between the plank and the wall?

Q6:

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

Q7:

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

Q8:

A 33 ft ladder leans against a building such that the angle between the ground and the ladder is . How high does the ladder reach up the side of the building?

Q9:

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.

Q10:

The base of a truck is 2 feet off the ground and a 15-foot ramp is used to load the truck. Find the angle the ramp makes with the horizontal ground.

Q11:

The base of a truck is 2 feet off the ground and a 20-foot ramp is used to load the truck. Find, to two decimal places, the angle the ramp makes with the horizontal ground.

Q12:

, , 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.

Q13:

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

Q14:

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

Q15:

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

• A
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Q16:

In the given figure, , , and . Work out the height of the triangle to 2 decimal places. Q17:

In the given figure, , , and . Work out the height of the triangle to 2 decimal places. Q18:

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.

Q19:

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

Q20:

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.

Q21:

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
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• E

Q22:

In the given figure, has been extended to the point such that and are perpendicular. Work out the length of to two decimal places. Q23:

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

Q24:

An airplane is flying to a city 200 miles away. Given that the destination city is 25 miles north of the departure city, how many degrees north of east should the airplane fly? Round your answer to two decimal places.

Q25:

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