Question

The angle of elevation of the top of a hill is 30 degree from a point on a ground .on walking 1 km towards hill angle of elevation is 45 degree calculate the height of the hill

Answer 1

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Answer 2

Answer: 1.37 Km

Explanation:

• Given, angle of elevation from point P to the top of the hill= 30°
• After moving 1 Km the angle of elevation from point Q to the top of hill= 45°
• In the given figure AB is the height of the hill and QB is x Km.
• In ΔPAB,

         tan 30°= $\frac{AB}{x+1}$

     ⇒ $\frac{1}{\sqrt{3} }=\frac{AB}{x+1}$

     ⇒ $AB=\frac{x+1}{\sqrt{3} }$

• In ΔQAB,

        tan 45°= $\frac{AB}{x}$

     ⇒ AB=x

• From both the above equations of AB we see,

             $\frac{x+1}{\sqrt{3} } = x$

       ⇒ $\sqrt{3}x-x=1$

       ⇒ x= $\frac{1}{0.732}$

        ∴ x=1.37 Km.

       ∴ AB= 1.37 Km

• Hence, the height of the hill is 1.37 Km.

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