Question

If the distance of a point from the base of a building is 15m and angle of elevation to its top from that point is 60°.then, what is the height of the building.

a)25m
b)26m
c)31m
d)18m​

Answer 1

done if I have done any mistake than forgive me

and sorry

Answer 2

Given:

Distance of the base from the reference point = 15 m

The angle of elevation to the top of the building = 60°

To Find:

The height of the building

Solution

• Let a point P be 15 m away from the base (Q) of a building.
• Le the base distance be denoted as PQ= 15m.
• Let the height of the building be denoted as QR = 'h' m.

• If the angle of elevation and base length is given, we can use the trigonometric function tanФ to find the height.
• TanФ is the ratio between sinФ and cosФ, i.e, between the height and the base of a right-angle triangle.

1. List the dimensions of the given triangle.

• As per assumptions made, we have ΔPQR,

where PQ is the base. PQ= 15 m

           QR is the height. QR = 'h' m

           PR is the hypotenuse

          ∠PQR = 90°                

         ∠QPR = 60°            (given)

2. Apply tanФ function to find the height of the building.

• TanФ is given as:

                             tanФ = $\frac{height}{base\\}$

                         ⇒ tan60° = $\frac{QR}{PQ}$

                         ⇒ √3 = $\frac{h}{15}$                              (tan60° = √3)

                         ⇒ h = 15√3 m

                        ⇒ h = 25.98 ≈ 26 m

Thus the height of the building is 26 m.

The correct option is b) 26 m.