Question

To measure a stone face carved on the side of a​ mountain, two sightings 750 feet from the base of the mountain are taken. if the angle of elevation to the bottom of the face is 33° and the angle of elevation to the top is 3636°​, what is the height of the stone​ face

Answer 1

Answer: 57.8512 feet (approx)

Step-by-step explanation:

Let h be the height of the stone face.

The angle of elevation from one sight to the bottom of face that is 750 feet far from the base of the mountain is 33°

⇒ The distance of the base of the stone face from the base of the mountain = $750\times tan 33^{\circ}=750\times 0.64940759319=487.055694898$

The angle of elevation from another sight to the top of face is 36° that is also 750 feet away from the base of the mountain,

Therefore,

The distance of the top of the stone face from the base of the mountain  = (h + 487.055694898) feet

By the trigonometry,

$\frac{h + 487.055694898}{750}=tan36^{\circ}$

$h + 487.055694898=0.726542528\times 750$

$h =544.906896004-487.055694898=57.8512011059\approx 57.8512$

Therefore, the height of the stone face is 57.8512 feet (approx).