Answer:
36 meters
Step-by-step explanation:
You are given an angle and the length of the side adjacent. You want to find the length of the side opposite, so the relevant trig relation is ...
Tan = Opposite/Adjacent
Setup
The height of Yuri's balcony is the sum of the heights of Kim's balcony and the height of Yuri's balcony above that. Each of those height is the side opposite a given angle in a right triangle. These can be found by solving the tangent relation for the opposite side:
Tan = Opposite/Adjacent
(Adjacent)(Tan) = Opposite
height of Kim's balcony = (30 m)tan(40°)
height above Kim's balcony = (30 m)tan(20°)
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height of Yuri's balcony = height of Kim's + height above Kim's
height of Yuri's balcony = (30 m)tan(40°) +(30 m)tan(20°)
height of Yuri's balcony = (30 m)(tan(40°) +tan(20°))
Evaluation
height of Yuri's balcony ≈ (30 m)(0.8391 +0.3640) ≈ 36.092 m
The height of Yuri's balcony is about 36 meters.
