# Trig word problem

#### sinjid9

From a balloon the angle of depression of a ground marker is 35 degrees. From a point 200m higher the angle of depression is 54 degrees. Find the distance from the marker to the point on the ground directly beneath the balloon.

How do you solve this?

#### bigwave

there are several ways to solve this

one is find the distance from the marker to the balloon which would be an hypotenuse then you find the base which the distance from the marker to the spot directly under the balloon.

some useful tools here is the law of sine's and the Pythagoran therom

do you want to see the steps to do this

#### sinjid9

Could you do this using trigonometric ratios? cause I think my teacher expects that.

#### bigwave

Could you do this using trigonometric ratios? cause I think my teacher expects that.
Law of Sines is one the trigonometric ratio's you can use

$$\displaystyle \frac{\sin{\alpha}}{a} = \frac{\sin{\beta}}{\beta} = \frac{\sin{\gamma}}{\gamma}$$

again, several ways to solve this but
do you know how to use the law of sines with this

#### sinjid9

I know how to use it but don't you need a angle and the side length opposite to it?

#### bigwave

I know how to use it but don't you need a angle and the side length opposite to it?
other angles are easily derived, from geometric theroms. the interior angles are $$\displaystyle 36^o, 126^o$$ and $$\displaystyle 18^o$$

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#### sinjid9

I got around 295m but the sheet says its 285m...

#### bigwave

actually I got 307.89 which isn't the given answer either.

$$\displaystyle \frac{\sin{18^o}}{200m} = \frac{\sin{126^o}}{\gamma} \Rightarrow \gamma = 523.61m$$

$$\displaystyle \Rightarrow \left(523.61\right) \cos{54^o} = \beta = 307.89$$

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