Question

From a point 100m above a lake the angle of elevation of a stationary helicopter is 30 and the angle of depression of reflection of the helicopter in the lake is 60 ..find the height of the helicopter.

Answer 1

hope this will help you

Answer 2

Answer: The height of the helicopter is 200 meters.

Step-by-step explanation:

Let the height of the helicopter from the horizontal line respect to the point = x,

Thus, the height of the helicopter =  (100 + x) meters

Also, let y be the distance of the point to the vertical line that shows the distance of the helicopter from the lake.

⇒ The distance of the reflection of the helicopter from the point = (100+x) meters

Now, By the below diagram,

$tan 60^{\circ}=\frac{100+100+x}{y}$

$\implies \sqrt{3}=\frac{200+x}{y}$  

$\implies y\sqrt{3}=200+x$

$\implies y = \frac{200+x}{\sqrt{3}}$ ------(1)

Now, Again by the diagram,

$tan30^{\circ}=\frac{x}{y}$

$\implies \frac{1}{\sqrt{3}}=\frac{x}{y}$

$\implies y = x\sqrt{3}$ -----(2)

From equation (1) and (2),

We get,

$x\sqrt{3}=\frac{200+x}{\sqrt{3}}$

$\implies 3x = 200+x$

$\implies 2x= 200\implies x = 100$

Hence, the height of the helicopter =  (100 + x) meters = (100+100) meters = 200 meters.