Question

The width of a road is $b$' feet on one side of which there is a window $h$' feet height. A building stands on another side of the road and subtends an angle $\theta$ at the window. Then the height of the building is

• A. $\frac{(b^2+h^2)}{b\cos \theta +hsin\theta }$
• B. $\frac{(b^2+h^2)sin\theta }{b\cos \theta +hsin\theta }$
• C. $\frac{(b^2+h^2)sin\theta }{h}$
• D. $\frac{(b^2+h^2)sin\theta }{b\cos \theta -hsin\theta }$

Answer 1

The correct option is B $\frac{(b^2+h^2)sin\theta }{b\cos \theta +hsin\theta }$

Using sine law, we get $\frac{H}{sin\theta }=$ $\frac{\sqrt{b^2+h^2}}{sin(90°+\alpha -\theta )}$

$\frac{H}{sin\theta }=$ $\frac{\sqrt{b^2+h^2}}{cos(\alpha -\theta )}$

$\frac{H}{sin\theta }=$ $\frac{\sqrt{b^2+h^2}}{cos\theta .cos\alpha +sin\theta .sin\alpha }$

$cos\alpha =$ $\frac{b}{\sqrt{b^2+h^2}}$

$sin\alpha =$ $\frac{h}{\sqrt{b^2+h^2}}$

$\therefore$ $\frac{H}{sin\theta }=$ $\frac{b^2+h^2}{bcos\theta +hsin\theta }$

$H=$ $\frac{(b^2+h^2)sin\theta }{bcos\theta +hsin\theta }$