Question

From a hot-air balloon, Guadalupe measures a 31 degree angle of depression to a landmark thats 316 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary

Answer 1

We will first sketch the problem

Let x be the vertical distance above the ground

Using the trigonometric ratio;

`\tan \theta=(opposite)/(adjacent)`
`\tan 31=(x)/(316)`

cross-multiply

`x=316\tan 31^o`
`x\approx189.9`