The angle of elevation of the sun is 22∘. A 6ft tall man is standing in the shadow of a 76 ft tall tree so that the tips of their shadows coincide. Sketch the situation. Find the distance between the man and the tree? rounded to the nearest foot

Answer: 173.26 ft = 173 ft

Step-by-step explanation:

h tree: 76 ft

h man: 6 ft

As we can see on the sketch, they form a right triangle, so:

tan 22 = 76/y ⇒ 0.404 = 76/y ⇒ y = 76*0.404 ⇒ y = 188.11 ft

tan 22 = 6/x ⇒ 0.404 = 6/x ⇒ x = 6*0.404 ⇒ x = 14.85 ft

distance between the man and the tree = y - x = 188.11 - 14.85 = 173.26 ft