Awoman entering an outside glass elevator on the ground floor of a hotel glances up to the top of the building across the street and notices that the angle of elevation is 51°. she rides the elevator up three floors (60 feet) and finds that the angle of elevation to the top of the building across the street is 34°. how tall is the building across the street? (round to the nearest foot.)

Let us say that,

60 + x = the full length of the building across the street

x = the length of the building from three floors (60 ft)

 

We can calculate for the length of the building using the trigonometric function tan. Where tan is:

tan θ = opposite side / adjacent side

In this case, the opposite side is the length of the building starting from the woman’s ground point while the adjacent side is the length of the street.

tan 51 = (60 + x) / a                --->      a = (60 + x) / tan 51

tan 34 = x / a                           --->      a = x / tan 34

Equating the two equations:

(60 + x) / tan 51 = x / tan 34

60 + x = (tan 51 / tan 34) x

0.8308 x = 60

x = 72.22 ft

 

Therefore,

60 + x = 132.22 ft

The building across the street is around 132 ft tall.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12