Question

True or False
An object is observed from three points A, B, C in the same horizontal plane passing through the base of the object. The angle of elevation at B is twice and at C is thrice that at A. If AB = a, BC = b, then the height of the object is $\frac{a}{2b}\sqrt{(a+b)(3b-a)}$.

• A. True
• B. False

Answer 1

The correct option is A True

$h=asin2\theta =2asin\theta cos\theta$
(Also by sine rule on $\Delta PBC$)
$\frac{a}{sin(\pi -3\theta )}=\frac{b}{sin\theta }$
$\therefore \frac{a}{b}=\frac{3sin\theta -4si{n}^3\theta }{sin\theta }\therefore si{n}^2\theta =\frac{3b-a}{4b}$
$\therefore co{s}^2\theta =\frac{a+b}{4b}$ put in the above.