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# Sine, Cosine, and Tangent- Word Problems (Grades 11-12)

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## Sine, Cosine, and Tangent- Word Problems

1.
Meryl is standing 100.5 feet from the Eiffel Tower and sees a bird land on the top of the tower. If the angle of elevation from Meryl to the top of the Eiffel Tower is close to 84.6°, how tall is the tower, to the nearest foot?

2.
The length of a tree’s shadow is 20 feet when the angle of elevation to the Sun is 40°. How tall is the tree, to the nearest hundredths?

3.
A building code states that a set of stairs cannot rise more than 72 cm for each 100 cm of run. What is the maximum angle at which the stairs can rise? Round your answer to the nearest degree.

4.
Katie is flying a kite on a windy day. When the kite is 15 m above the ground, the string of the kite makes an angle of $50deg$ with the horizontal. If Katie is holding the string 1 m above the ground, how much string has she released? Round your answer to the nearest tenth.

5.
A tree that is 9.5 m tall casts a shadow that is 3.8 m long. What is the angle of elevation of the Sun, to the nearest degree?

6.
Sharon and Lewis are 520 m apart. As Brandon flies overheard in an airplane, they measure the angle of elevation of the airplane. The airplane is between Sharon and Lewis. Sharon measures the angle of elevation to be $63deg$. Lewis measures it to be $36deg$. What is the altitude of the airplane?

7.
From a distance of 300 m, Susan looks up at the top of a lighthouse. The angle of elevation is $5deg$. Determine the height of the lighthouse to the nearest meter.

8.
Madeleine flies a kite on a 17 m string at an inclination of $63deg$. What is the height, $h$, of the kite above the ground? If Madeleine's friend Sophie stands directly below the kite, calculate the distance, $d$, between the two friends. Calculate both distances to the nearest hundredths meter.

9.
An airplane is flying 4000 feet above the ground. If the angle of depression to the airport runway is $12deg$, how far is the airplane from the runway, to the nearest foot? (I.e. what is the "ground distance"?)

10.
A 9 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of the wall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.

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