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**Suzie** I'm in a geometry class and learning trig. Here's a few problems that are confusing me a bit. Any help solving these is appreciated!!

for all of these problems, make a sketch of the right triangle formed by the problem situation and label the known angle, the side opposite the angle, the side adjacent to the angle, and the hypotenuse.

A little boy is flying a kite. The string of the kite makes an angle of 30 degrees with the ground. If the height of the kite is h = 12 m, find the length of the string that the boy has used.

$\displaystyle \textcolor{red}{\sin{\theta} = \frac{opposite \, side}{hypotenuse}}$

$\displaystyle \textcolor{red}{hypotenuse = \frac{opposite \, side}{\sin{\theta}}}$

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A building 14.5 m tall casts a shadow of 11.4 m along the level ground. At what angle do the rays of the sun hit the ground (to the nearest degree)?

$\displaystyle \textcolor{red}{\tan{\theta} = \frac{opposite \, side}{adjacent \, side}}$

$\displaystyle \textcolor{red}{\theta = \tan^{-1}\left(\frac{opposite \, side}{adjacent \, side}\right)}$

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A balloonist records her altitude as 1208 meters. At the same time she measures the angle of depression of the landing spot to be 17 degrees. How far away, to the nearest meter, is the landing sot from a point on the ground vertically below the balloon?

$\displaystyle \textcolor{red}{\tan{\theta} = \frac{opposite \, side}{adjacent \, side}}$

$\displaystyle \textcolor{red}{adjacent \, side = \frac{opposite \, side}{\tan{\theta}}}$

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An observer in a lighthouse is 66 feet above the surface of the water. The observer sees a ship and finds the angle of depression to be 7 degrees. Estimate the distance of the ship from the base of the lighthouse. Round the answer to the nearest 5 feet.

same ratio as the balloon problem