from a point P on the ground the angle of elevation of the top of the tower is 30° and that of the top of the flagstaff fixed on top of the tower is 60° if the length of the flagstaff is 5 metre find the height of the tower.
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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
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