CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The angle of elevation of the top of a tower from a certain point is $$\displaystyle 30^{0}$$ If the observer moves 20m towards the tower the angle of elevation of the top of the tower increases by $$\displaystyle 15^{0}$$ The height of the tower is


A
17.3m
loader
B
21.9m
loader
C
27.3m
loader
D
30m
loader

Solution

The correct option is C $$27.3$$m
Let AB be the tower and C and D be the point of observation 
Given  CD =20 m And $$\angle BCA=30^{0}$$ and $$ \angle BDA=30+15=45^{0}$$
Let height of tower is h
In triangle BAD
$$tan 45^{0}=\frac{AB}{AD}\Rightarrow 1=\frac{h}{AD}\Rightarrow AD=h$$
In triangle BAC
$$tan 30^{0}=\frac{AB}{AC}$$ ( AC=CD+AD)
$$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{20+h}$$
$$\Rightarrow \sqrt{3}h=20+h$$$$\Rightarrow \sqrt{3}h-h=20$$
$$\Rightarrow h(1.732-1)=20$$
$$\Rightarrow h=\frac{20}{0.732}=27.3$$

635799_374529_ans_bbe1de320fc84b8999a7b2bb7500dcb9.png

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image