Question

A lamppost is situated at the middle point M of the side AC of a triangular plot ABC with BC = 7 m, CA = 8 m and AB = 9 m. Lamppost subtends an angle 15° at the point B. Find the height of the lamppost.

Answer 1

Answer:

7(2 - √3)

Step-by-step explanation:

Let MP be the lamp post and h be the height, M will be the midpoint of AC.

 CM = 1/2 AC = 1/2 x 8 = 4 m

Applying cosine rule for triangle ABC we have

 Cos C = 7^2 + 8^2 - 9^2 / 2 x 7 x 8

Cos C = 32/112 = 2/7

Again from triangle BMC,

Cos C = 7^2 + 4^2 - BM^2 / 2 x 7 x 4

         = 2/7

BM^2 = 7 m

From triangle BMP,

angle BMP = 90 degree and angle MBP = 15 degree

tan 15 degree = MP/BM

 tan(45 -30) = tan 45 - tan 30 /1 + tan 30 tan 45

 = √3 - 1/√3 + 1

Rationalizing the denominator we get

(√3 -1)^2 / 3-1

3 + 1 - 2√3 /2 = (2 - √3)

So (2 - √3) = h/7

or h = 7(2 - √3)

Answer 2

Step-by-step explanation:

refer to the image ......