The angle of elevation from a point on the ground to the top

The angle of elevation from a point on the ground to the top of a pyramid is 35 degree 10\' The angle of elevation from a point 115 feet farther back to the top of the pyramid is 28 degree 20\'. Find the height of the 28 20 35 10 pyramid. What is the height of the pyramid? ft (Round to the nearest integer.)

Solution

Let height of pyramid be h feet

In smaller traingle

tan 35^o 10\' = h/x

0.704 = h/x

h = 0.704x..........1

In bigger triangle

tan 28^o 10\' = h/ (115+x)

putting the value of h, we get

0.5344 = 0.704x / 115+x

0.5344 ( 115+x) = 0.704 x

61.456 + 0.5344x = 0.704 x

0.704x - 0.5344x = 61.456

0.1696x = 61.456

x = 362feet

h=0.704x

putting value of x , we get

h = 0.704 * 362

= 255 feet............height of pyramid