Question

application of trignometry 16​

Answer 1

Answer:

height of the tower= 6m

Step-by-step explanation:

Let h be the height of the tower

and let α be the angle of elevation

Since the angles are complementary, they add up to 90°.

Therefore, the angle of elevations are: α and 90-α

Refer to the drawing shown below.

tanα = h/4

tan(90-α) = h/9

According to trig identities,

tan(90-α) = cotα

Therefore,

cot α = h/9

1/ tan α = h/9

So, tan α = 9/h

Since tan α has two different values(that is h/4 and 9/h), make them equal.

So h/4 = 9/h

h^2 = 36

Therefore h= 6m