How do i solve for the answer?

Question

To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 31∘.

From a point that is 300 feet closer to the building, the angle of elevation (at ground level) to the top of the building is 57∘. If we assume that the street is level, use this information to estimate the height of the building. Round to the nearest foot.

Answer 1

Let y = the height of the building. Let x = the distance from the closer point to the base of the building.

tan(31°) = y/(300+x)

tan(57°) = y/x

y = xtan(57°) from second equation and substitute that in for y in the first equation

tan(31°) = (xtan(57°))/(300+x)

Solve for x:

(300+x)(tan(31°) = xtan(57°)

300tan(31°) + xtan(31°) - xtan(57°) = 0

x = -300(tan(31°))/((tan(31°)-tan(57°))

x = -300(.6)/(.6-1.54) ≈ 191 feet

Solve for y

y = xtan(57°) = 191(1.54) = 294 feet