Question

In a triangular plot ABC with BC = 7m, CA-8m and AB =9m a lamp post is situated at the middle
point E of the side AC and subtends an angle tan '3 at the point B, the height of the lamp post is
​

Answer 1

Given:

In a triangular plot ABC with BC = 7m, CA-8m and AB =9m.

A lamp post is situated at the middle  point E of the side AC.

It subtends an angle  $tan^{-1}$3 at the point B.

To Find:

The height of the lamp post .

Solution:

In the triangle ABC, we can apply cosine rule.

• 2ab cos C = a² + b² - c²
• 2 x 7 x 8 cosC = 7² +  8² - 9²
• cosC = 32/112 = 2/7
• Also, consider the small ΔBCE,
• 2 x 7 x 4 x cosC = 7² + 4² - L²
• 2 x 7 x 4 x 2/7 = 65 - L²
• L² = 65 - 16 = 49
• L = 7m

By considering the pole height to be h,

• tan ( $tan^{-1}$3) = h/L
• h = 3L = 21m.

Height of the pole is 21m

Answer 2

Answer:

In the triangle ABC, we can apply cosine rule.

2ab cos C = a² + b² - c²

2 x 7 x 8 cosC = 7² + 8² - 9²

cosC = 32/112 = 2/7

Also, consider the small ΔBCE,

2 x 7 x 4 x cosC = 7² + 4² - L²

2 x 7 x 4 x 2/7 = 65 - L²

L² = 65 - 16 = 49

L = 7m

By considering the pole height to be h,

tan ( tan^{-1}tan

−1

3) = h/L

h = 3L = 21m.