Question

an observer 1.2m tall is 28.2m away from the foot of the tower. the angle of elevation of the top of the tower from his eye is 60'.what is the height of the tower.

Answer 1

Hope this helps.....

Answer 2

Given,

Height of an observer = 1.2 meters

Distance of the observer from the foot of the tower = 28.2 meters

The angle of elevation of the top of the tower from the observer's eye = 60°

To find,

The height of the tower.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the height of the tower from above the observer is x meters.

=> the total height of the tower = height of the observer + the height of the tower from above the observer

=> the total height of the tower = (1.2 + x) meters

{Equation-1}

Now, according to the question;

The imaginary line joining the top of the observer with the tip of the tower forms the hypotenuse of a right-angled triangle whole perpendicular is represented by the height of the tower from above the observer and the base is represented by the imaginary line representing the horizontal distance of the observer from the foot of the tower. The acute angle opposite to the perpendicular is 60°.

Now, as per trigonometry, on applying the Tan ratio formula for the given angle, we get;

Tan 60° = (length of the side opposite to the considered angle)/(length of the side adjacent to the considered angle, other than the hypotenuse) = (length of the perpendicular)/(length of the base)

=> Tan 60° = (the height of the tower from above the observer)/(the horizontal distance of the observer from the foot of the tower)

=> √3 = x/(28.2)

=> x = 28.2 × √3 = 28.2 × 1.73 = 48.8 meters

=> the height of the tower from above the observer = 48.8 meters

Now, according to the equation-1;

The total height of the tower

= (1.2 + x) meters

= (1.2 + 48.8) meters

= 50 meters

Hence, the total height of the tower is 50 meters.