Question

A pole that is 3.1m tall casts a shadow that is 1.46m long. At the same time, a nearby building casts a shadow that is 36.75m long. How tall is the building?

Answer 1

you have to find the angle of sunlight and the pole , which then cast a shadow
length of the pole is equal to 3.1m
creating a hypotenuse of 4.52m
the angle will be
sin@ = opposite side / hypotenuse
= 1.46/4.52
= 0.32 that's 18.66 °
now for the building sin18.66° = opposite/hypotenuse
0.32 = 36.75/ hypotenuse
hypotenuse = 114.84 m
thus using Pythagoras theorem
114.84*114.84 = 36.75*36.75 + x^2
which comes around = 108.8 roughly 109 metres long