Question

If the angles of depression and elevation of the top of a tower of height $h$ from the top and bottom of a second tower and $x$ and $y$ respectively, then the height of the second tower is

• A. $h(\cot y+\cot x)$
• B. $h(\tan x+\tan y)$
• C. $h(1+\tan x\cot y)$
• D. $h(\tan y\cot x+1)$

Answer 1

The correct option is C $h(1+\tan x\cot y)$

From $△ABC,b=h\cot y$
$\Rightarrow AD=h\cot y$
From $△AED,x_1=h\cot y\tan x$
$\therefore heightEC=h+h\cot y\tan x$
$=h(1+\cot y\tan x)$.