Question

A window in a building is at a height of 10 m above the ground the angle of depression of point p of the ground from the window is 30 the angle of elevation of the to of the building from the point p is 60. Find the height of the building

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Let AB be a building of height 10m and C be the position of the helicopter, hovering at height h over it's top. Let P be the point of observation on the ground.

Then,

From right ∆ABP, we have

$\longrightarrow$$\sf\green{tan30°=\frac{AB}{PB}}$

$\longrightarrow$$\sf\green{\frac{1}{√3}=\frac{10}{PB}}$

$\therefore$ $\sf\green{PB=10√3m}$

From right ∆CBP, we have

$\longrightarrow$$\sf\green{tan60°=\frac{BC}{PB}}$

$\longrightarrow$$\sf\green{√3=\frac{BC}{10√3}}$

$\therefore$ $\sf\green{BC=10√3×√3}$

$\longrightarrow$$\sf\green{30m}$

Hence, the height of the helicopter above the ground is 30m.