From his eye, which stands 1.55 meters above the ground, Tyler measures the angle of elevation to the top of a prominent skyscraper to be 57^{\circ} ∘ . If he is standing at a horizontal distance of 112 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.

We can use trigonometry to solve this problem. If we call the height of the skyscraper "h" and the horizontal distance from Tyler to the base of the skyscraper "x", we can create a right triangle with the following sides:

The height of the skyscraper (h)

The horizontal distance from Tyler to the base of the skyscraper (x = 112m)

The distance from Tyler's eye to the top of the skyscraper (the hypotenuse of the triangle)

We know that the angle of elevation from Tyler's eye to the top of the skyscraper is 57 degrees. We can use the tangent function to find the height of the skyscraper:

tan(57) = h/x

h = x * tan(57)

h = 112m * tan(57)

h ≈ 312.39m

The height of the skyscraper is approximately 312.39 meters, or 312.39m.