Question

During a visit to New York City, Lil decides to estimate the height of the Empire State Building (see figure below). She measures the angle θ of elevation of the spire atop the building as 17°. After walking x = 9.28 ✕ 102 ft closer to the iconic building, she finds the angle to be 20.9°. Use Lil's data to estimate the height h of the Empire State Building. (Enter your answer to at least the nearest

Answer 1

Tan17 = h/d.
h = d*Tan17.

Tan20.9 = h/(d-928).
h = (d-928)*Tan20.9.

d*Tan17 = (d-928)*Tan20.9.
d = ?.

h = d*Tan17.

Answer 2

It's easy if you
(a) draw a diagram
(b) review your trig functions

Then it's clear that if the height is h,

h cot17° - h cot20.9° = 928

Now just find h.

Answer 3

Divide both sides by Tan17:
d = 1.25*(d-928),
d = 4636.4 Ft.

h = d*Tan17 = 4636.4 * Tan17 =

Answer 4

1st: Split the two angle from the ground to the spire atop into two right triangles
2nd: take tangent of the two angles and multiply them --> tan(17)time tan(20.9)=-6.71696
3rd: 9.28x10^2=928
4th: multiply 928time-6.71696= -6233.3
5th: htan (17)-htan(20.9)=-6233.3
6th: factor out the h-->h(tan(20.9)-tan(17))=-6233.3
7th:h(-5.4)=-6233.3
8th divid-6233.3 by -5.4=1154ft
9th: the answer is1,157 feet