# Worksheet: Applications of the Inverse Trigonometric Function

In this worksheet, we will practice using inverses of trigonometric functions to solve both mathematical and real-life problems.

Q1:

A rocket took off from a launchpad and traveled directly upward. When the rocket was 15 miles up, one of the astronauts looked down at the mission control center, which is 2 miles away from the launchpad. What was the angle of depression from her to the mission control center? Round your answer to two decimal places.

Q2:

Find the exact value of in radians.

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Q3:

Find the exact value of in radians.

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Q4:

A boat is 530 metres away from the base of a 400-metre high cliff. Find the angle of depression of the boat from the top of the cliff giving the answer in radians to three decimal places.

Q5:

Find the exact value of in radians.

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Q6:

Find the exact value of , in radians in terms of , which is located in the 1st quadrant.

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Q7:

A woman stands 6 feet from a vertical wall. A footlight on the ground 3 feet from where she is standing is switched on. If the woman is 5 feet tall and her shadow is 15 feet tall, what angle does the light make with the horizontal? Give your answer to two decimal places.

Q8:

A 90-foot tall building has a shadow that is 2 feet long. What is the angle of elevation of the sun?

Q9:

A ladder is leaning against a vertical wall such that the top is 9 m above the ground and its base is 3 m from the bottom of the wall. Find the measure of the angle between the ladder and the ground. Give your answer to two decimal places.

Q10:

A rocket is launched vertically upward. A woman, standing 4 miles from the launch pad, watches its flight. What is the angle of elevation of the rocket from the woman when its altitude is 11 miles?