Question

when the sun is 77 degrees above the horizon, a building casts a shadow 25ft long . how tall is the building. (round to the nearest foot)?

Answer 1

Answer: The height of the building is 108 ft

The following is the illustration of the above question

The height of the building can be calculated using SOH CAH TOA

opposite side = x ft

Adjacent sides = 25 ft

`\begin{gathered} \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{Tan 77 = }(x)/(25) \\ \text{Cross multiply} \\ x\text{ = tan 77 x 25} \\ \text{Tan 77 = 4.33} \\ x\text{ = 4.33 x 25} \\ x\text{ = 108.286 ft} \\ x\text{ = 108 ft} \end{gathered}`