Question

Two boats 1200 feet apart measures an angle of elevation of 35 degree and 42 degree to the top of a lighthouse. how tall is the lighthouse?

Answer 1

Let $h=$ the height of lighthouse.

The ditance from the first boat to the foot of the lighthouse is $\dfrac{h}{\tan 35\degree}.$

The distance from the second boat to the foot of the lighthouse is $\dfrac{h}{\tan 42\degree}.$

Then

$$\dfrac{h}{\tan 35\degree}-\dfrac{h}{\tan 42\degree}=1200$$

$$h=\dfrac{1200\tan 35\degree\tan 42\degree}{\tan 42\degree-\tan 35\degree}=3779(ft)$$

$$3779ft=1152m$$

I think the answer has no sense.