Question

Please help 10 points

Answer 1

Therefore h = 22.75 ft

Explanation:

We know that

`tan\theta =(altitude)/(base)`

Using this for the triangles

For the small triangle

`tan \theta =(6(1)/(2) )/(9)`

`\Leftrightarrow tan \theta =((13)/(2) )/(9)`

`\Leftrightarrow tan \theta =\frac{13} {18}`

Again for the bigger triangle

`tan \theta =(h)/(31(1)/(2) )`

`\Leftrightarrow tan \theta =(h)/((63)/(2) )`

`\Leftrightarrow tan \theta =(2h)/(63)`

Therefore

`(2h)/(63) =(13)/(18)`

`\Leftrightarrow h=(13 * 63)/(18 * 2)`

`\Leftrightarrow h=(819)/(36)`

`\Leftrightarrow h = 22.75` ft

Therefore h = 22.75 ft