The angle of depression from 100-meter tower to the top and botto
|
The angle of depression from 100-meter tower to the top and bottom of a house is 30° and 60° respectively. What is height of house?
A. <span class="math-tex">\(\frac{{200}}{3}\)</span>
B. 100
C. <span class="math-tex">\(\frac{{100}}{3}\)</span>
D. 200
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Let AB = h
In ΔBCE
\(tan60^\circ = \frac{{EC}}{{BC}}\)
\(\sqrt 3 = \frac{{100}}{{BC}}\)
\(BC = \frac{{100}}{{\sqrt 3 }}\) -----(i)
In ΔAED
\(tan30^\circ = \frac{{ED}}{{AD}}\)
\(\frac{1}{{\sqrt 3 }} = \frac{{100 - {\rm{h}}}}{{{\rm{BC}}}}\)
BC = (100 - h) × \(√3\)
√
\(BC = \frac{{100}}{{\sqrt 3 }}\)
(100-h)3 = 100
\(h = \frac{{200}}{3}\)
