Question

from a point P on the ground the angle of elevation of the top of a tower is 30° and that of the top of the flagstaff fixed on the top of the tower is 45 degree if the length of the flagstaff is 5 M find the height of the tower used under root 3 is equal to 1.732

Answer 1

Answer:

7.393 M

Step-by-step explanation:

Let the height of the tower be x then the total height of the tower and the flag is :

Total height = x + 5

Two right angled triangles are formed having a common base.

Let the base length be b.

Using Tan as the main trigonometric ratio.

Tan = opposite / adjacent

Tan 30 = x / b

b = x / Tan 30

Tan 45 = (x + 5) / b

b = (x + 5) / Tan 45

Since the b's are equal :

x/Tan 30 = (x + 5)/Tan 45

x Tan 45 = xTan 30 + 5 Tan 30

0.8541x = 0.5095x + 2.5476

0.8541x - 0.5095x = 2.5476

0.3446x = 2.5476

x = 7.393 m

The height of the tower is thus 7.393 m.

Answer 2

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