Question

a stairs stands vertically on the ground. from a point on the ground. which is 10m away from the top of the foot of the tower, the angle of elevation of the top of the stairs is found to be 30°. find the height of the stairs​

Answer 1

A stairs which is 10 m away from the foot of the tower and the angle of elevation of the top of the stairs is found to be 30°, then the height of the stairs is [10/√3] m or 5.77 m .

Step-by-step explanation:

The distance between the foot of the stairs and that of the tower = 10 m  

The angle of elevation of the top of the stairs, θ = 30°

Let the height of the stairs be denoted as “h” meter.

Now, from the figure attached below, let’s consider ∆ABC and apply trigonometry properties of the triangle to it, then we will get

tan θ = $\frac{Perpendicular}{Base}$ = $\frac{AB}{BC}$

here AB = h = height of the stairs & BC = 10 m = distance between the stair and the tower  

By substituting the given values to the above property, we get

tan 30° = h / 10

⇒ 1/√3 = h/10 …… [since tan 30° = 1/√3]

⇒ h = 10/√3 m

⇒ h = [10/1.732] m  

⇒ h = 5.77 m

Thus, the height of the stairs is [10/√3] m or 5.77 m.

Hope this is helpful!!!