Trigonometric Equations Question 174
Question: A flag-post 20m high standing on the top of a house subtends an angle whose tangent is $ \frac{1}{6} $ at a distance 70 m from the foot of the house. The height of the house is
Options:
A) 30 m
B) 60 m
C) 50 m
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \tan \alpha =\tan (\varphi -\theta ) $ $ \tan \alpha =\frac{1}{6}=\frac{\frac{20+h}{70}-\frac{h}{70}}{1+\frac{(20+h),h}{{{(70)}^{2}}}} $
$ \Rightarrow $ $ {{(70)}^{2}}+20h+h^{2}=(6)(70)(20) $
$ \Rightarrow $ $ h^{2}+20h+70(70-120)=0 $
$ \Rightarrow $ $ h^{2}+20h-(50),(70)=0 $
$ \Rightarrow $ $ h=\frac{-20\pm \sqrt{400+(4)(50)(70)}}{2}=50m $ .
BETA
