Question #296255

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.


1
Expert's answer
2022-02-11T11:10:13-0500

Solution:


BC = AD = 20 m

In triangle ABC,

tan45°=ABBC1=AB20AB=20 m\tan 45\degree=\dfrac{AB}{BC} \\ \Rightarrow 1=\dfrac{AB}{20} \\ \Rightarrow AB=20\ m

Now, AB = DC = 20 m

In triangle ADE,

tan20°=EDAD0.36397=ED20ED7.3 mEC=ED+DC=7.3+20=27.3 m\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


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