Question

Please help 10 points

Answer 1

Therefore h = 22.75 ft

Step-by-step explanation:

We know that

$tan\theta =\frac{altitude}{base}$

Using this for the triangles

For the small triangle

$tan \theta =\frac{6\frac{1}{2} }{9}$

$\Leftrightarrow tan \theta =\frac{\frac{13}{2} }{9}$

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

Again for the bigger triangle

$tan \theta =\frac{h}{31\frac{1}{2} }$

$\Leftrightarrow tan \theta =\frac{h}{\frac{63}{2} }$

$\Leftrightarrow tan \theta =\frac{2h}{63}$

Therefore

$\frac{2h}{63} =\frac{13}{18}$

$\Leftrightarrow h=\frac{13 \times 63}{18 \times 2}$

$\Leftrightarrow h=\frac{819}{36}$

$\Leftrightarrow h = 22.75$ ft

Therefore h = 22.75 ft