Find the height of a building which casts a 30-meter horizontal shadow when the angle of elevation of the sun is 60°?

Question

Complete computation with Pythagorean theorem

Answer 1

base of a right triangle is 30 meters

height of the right triangle = 30tan60=about 51.96

= about 52 meters

or if you're into the Pythagorean Theorem

the hypotenuse = twice the base = 60 meters

and

c^2 = b^2 + a^2

60^2 = 30^2 + height squared= a^2

a^2 = 3600-900 = 2700

a= sqr2700 = 10sqr27 = 30sqr3 = about 51.96 meters