Question

A man observes two vertical poles which are fixed opposite to each other on either side of the road If the width of the road is 90 feet and height of the pole in the ratio 1:2 also the angle of elevation of their tops from a point between the line joining the foot of the poles on the road 60°find the height of the poles
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Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given :

Two poles having heights in the ratio = 1 : 2

Width of the road between the poles = 90 feet

Angle of elevations of the tops of the poles = 60°

To find :

Height of the poles.

Solution:

Let the point O is x feet from a pole AB.

Therefore, OB = x feet

and OC = (90 - x) feet

From ΔABO,

tan(60)° = $\frac{AB}{BO}=\frac{a}{x}$ ----------(1)

Similarly, from ΔDCO,

tan(60)° = $\frac{DC}{CO}=\frac{b}{(90-x)}$ --------(2)

From equations (1) and (2),

$\frac{a}{x}$ = $\frac{b}{(90-x)}$

$\frac{a}{b}=\frac{x}{(90-x)}$

Since a : b = 1 : 2

$\frac{1}{2}=\frac{x}{(90-x)}$

90 - x = 2x

3x = 90

x = 30

Now substituting the value of x in equation (1),

$\sqrt{3}=\frac{a}{x}$

a = x√3

a = 30√3 ≈ 51.96 feet

Since, $\frac{a}{b}=\frac{1}{2}$

b = 2a

b = 2×(30√3)

b = 60√3 ≈ 103.92 feet

Therefore, heights of the poles are 51.96 feet and 103.92 feet