A ski lift is planned for the south slope of Mt Frissell in

A ski lift is planned for the south slope of Mt. Frissell in Connecticut. Point B is located directly below the top (point T), as shown in Figure 5.122. A surveyor determines that the angle of elevation from the start of the lift, S, to the end of the lift, T, to be 34.06 degree. Next, 1.000 Times 10^3 ft is measured on level ground to determine point P. If the angle of elevation to T at P is 27.77 degree, what is the approximate height of Mt. Frissell?

Solution

let height of Mt. frissell = h

from the figure

applying tan rule on first triangle OBS

tan 34.06 = h / x

.6760 = h/x

h = .6760 x

now for triangle OBP

tan 27.77 = h / x + 1000

.5265 = h / (x+1000)

h = .5265x + 526.5

.5265x + 526.5 = .6760 x

subtracting .5265x from both sides

526.5 = .1495x

x = 3521.74

h = .6760 x

h = .6760( 3521.74 ) = 2380.7 feet ( approx)

height of Mt. frissell = 2380.7 feet