Question

If the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complimentary, find the height of the tower.

Answer 1

Height of the tower is 6m

solution:

let height of tower is h

BC = 4m

BD = 9m

• If sum of two angles is 90° then

they are complimentary angles.

=> let <ADB =A then , < ACB = 90-A

• In triangle ABC

tan(90-A)= AB/BC=P/B=h/4

=> cot(A) = h/4 [tan(90-A)=cotA]

________(1)

• In triangle ABD

Cot(A) = B/P=BD/AB=9/h _____(2)

• Now, equating (1) & (2)

=> h/4=9/h

=> h² = 36

=> h = 6m

Answer 2

The height of the tower is 6 m

Explanation:

Given that the angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complimentary.

We need to find the height of the tower.

Let the height of the tower be AB

Let the length of BC is 4 and the angle of elevation at the point C is $\theta$

Let the length of BD be 9 and the angle of elevation at the point D is $90-\theta$

Let us consider the triangle ABC

$\cot \theta=\frac{4}{A B}$

Now, we shall consider the triangle ABD,

$\tan (90-\theta)=\frac{A B}{9}$

Since, $\tan \left(90^{\circ}-\theta\right)=\cot \theta$ , we get,

$cot \theta=\frac{A B}{9}$

 $\frac{4}{A B}=\frac{A B}{9}$

Cross multiplying, we get,

$A B^{2}=36$

 $A B=6$

Thus, the height of the tower is 6 m

Learn more:

(1) The angle of elevation of the top of a tower from two point at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. prove that the height of tower is 6m

brainly.in/question/2285814

(2) The angle of elevation of the top of a tower from two points at distance A and B metres from the base and in the same straight line with it are complementary prove that the height of the tower is root ab metre

brainly.in/question/6574394