Question

The angle of elevation of a cloud from a point $h$ metres above a lake is $\Theta$. The angle of depression of its reflection in lake is ${45}^{}$ The height of the cloud is

• A. $h\tan ({45}^0+\Theta )$
• B. $hcot({45}^0-\Theta )$
• C. $h\tan ({45}^0-\Theta )$
• D. $h\cot ({45}^0+\Theta )$

Answer 1

The correct option is A $h\tan ({45}^0+\Theta )$

$tan\theta =\frac{b}{d}$
tan 45 = $\frac{a}{d}$
$tan{\theta }_2\frac{b}{a}$
b + h = a - h
$tan{\theta }_2\frac{b}{b+2h}$
$\frac{1}{tan\theta }=1+\frac{2h}{b}$
$\frac{b}{24}=\frac{tan\theta }{1-tan\theta }$
$b=\frac{24tan\theta }{1-tan\theta }$
bfh = $\frac{h-htan\theta +2htan\theta }{1-htan\theta }=htan(\theta +45)$