Question

On a straight line passing through the foot of a tower, two points C and D are at distances of 4m and 16m from the foot respectively. if the angle of elevation from C and D of the top of the tower are complementary, then find the height of the tower.

Answer 1

just use trignometric identity
tan 90- theta is cot theta and 1/tan is cot
later just reverse rhs and LHS then equate equation 1 and 2 u will get the height

Answer 2

Answer:

Height of the tower is 8 meters

Step-by-step explanation:

We are given that,

Angle of elevation from C and D to the top of the tower are complementary as shown in the figure below.

That is, the sum of the angle of elevations from C and D to the top of the tower is 90°.

Let the angle of elevation from C = x°.

Then, angle of elevation from D = (90-x)°

Using the trigonometric forms for the angles, we have,

$\tan x= \frac{y}{4}$

and $\tan (90-x)=\frac{y}{16}$ i.e. $\cot (x)=\frac{y}{16}$ i.e. $\tan (x)=\frac{16}{y}$

Thus, equating the same values, we have,

$\frac{y}{4}=\frac{16}{y}$

i.e. $y^{2}=64$

i.e. y= ±8

Since, the height cannot be negative.

So, y= 8 meter

Hence, the height of the tower is 8 meters.