Answer to Question #296255 in Trigonometry for Gabe

Question

Two buildings are 20 m apart. The angle from the top of the shorter building to

the top of the taller building is 20°. The angle from the top of the shorter building

to the base of the taller building is 45°. What is the height of the taller building?

Make sure to include a diagram and concluding sentence.

Answer 1

Solution:

BC = AD = 20 m

In triangle ABC,

$\tan 45\degree=\dfrac{AB}{BC} \\ \Rightarrow 1=\dfrac{AB}{20} \\ \Rightarrow AB=20\ m$

Now, AB = DC = 20 m

In triangle ADE,

$\tan 20\degree=\dfrac{ED}{AD} \\ \Rightarrow 0.36397=\dfrac{ED}{20} \\ \Rightarrow ED\approx7.3\ m \\\therefore EC=ED+DC=7.3+20=27.3\ m$