Question

The height of tower is h meters. It is
found that, when walking 100 m
towards it in a horizontal line through
its base, the elevation of its top changes
from 30° to 60°, h is equal to​

Answer 1

Answer:

The height of the tower is 86.60 meters.

Step-by-step explanation:

Step 1: Let the distance from the second point to the foot of the pole be x.

Step 2 : the distance from the first point to the second point is 100 m.

We have two right angled triangles sharing the same height.

Step 3: The base of right angled triangle formed at 30° elevation is (100 + x) meters.

For 60° elevation the base length is x meters.

Step 4 : We will Tan as the trigonometric ratio for solving for both x and h.

Now :

Tan 60 = h/x

Tan 30 = h/(x + 100)

We can make h the subject of the equation in both cases.

h = x Tan 60..............1

h = (x + 100) Tan 30................2

Step 5 : Equate the two to solve.

xTan 60 = (x + 100) Tan 30

x × 1.7321 = 0.5774(x + 100)

1.7321x = 0.5774x + 57.74

1.7321x - 0.5774x = 57.74

1.1547x = 57.74

x = 50.004

Approximately 50 meters

Since we have x, we can now solve for h.

h = x Tan 60 = 50 × Tan 60

= 86.60 meters.

Therefore h = 86.60 meters.

Answer 2

Answer:

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