Question

A lamppost, CAB, bent at point A after a storm. The tip of the lamppost touched the ground at point C, as shown below: Triangle ABC has measure of angle C equal to 60 degrees, measure of angle ABC equal to 90 degrees, and length of BC equal to 14 feet. What is the height, in feet, of the portion AB of the lamppost?

Answer 1

You are given the side adjacent to ∠B and you want to find the length of the side opposite. The trig ratio that relates an angle to adjacent and opposite sides is ...

... tan(∠C) = Opposite/Adjacent = (AB)/(BC)

Multiplying by BC gives

... AB = BC×tan(∠C) = (14 ft)×(√3) ≈ 24.2 ft