Triangles And Properties Of Triangle Question 5
Question: The angle of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are $ 43{}^\circ $ and $ 47{}^\circ $ respectively. What is the height of the tower?
Options:
A) 40 m
B) 42 m
C) 45 m
D) 47 m
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ AB=h $ (height of the tower) $ BD=36m; $ $ BC=49m $ $ \angle D=47{}^\circ ; $ $ \angle C=43{}^\circ $ Now, in $ \Delta ABD, $ $ \tan 47{}^\circ =\frac{h}{36m} $ ? (i) and in $ \Delta ABC, $ $ \tan 43{}^\circ =\frac{h}{49m} $ $ \tan (90{}^\circ -47{}^\circ )=\frac{h}{49} $
$ \therefore \cot 47{}^\circ =\frac{h}{49} $ (ii) Multiplying equations (i) and (ii) $ \tan 47{}^\circ .\cot 47{}^\circ =\frac{h}{36}\times \frac{h}{49}=1=\frac{h^{2}}{36\times 49} $ $ h=6\times 7=42m $
$ \therefore $ Option [b] is correct
BETA
