Answer:
61.15 m
Step-by-step explanation:
From trigonometry :
Tan x = opposite / Adjacent
x = 28°
Tan 28 = distance from base to fire / height
0.5317094 = distance from base to fire / 115
distance from base to fire = 115 * 0.5317094
distance from base to fire = 61.15 m
The distance from the fire to the base of the tower is required.
The distance to the fire from the base of the tower is 216.3 meters which has been found using trigonometric ratios.
The angle of depression is 28°.
b = The height of the tower = 115 meter
p = The distance to the fire from the base of the tower
[tex]\theta=90-28=62^{\circ}[/tex]
From the trigonometric ratios we get
[tex]\tan\theta=\dfrac{p}{b}\\\Rightarrow p=b\tan\theta\\\Rightarrow p=115\tan62^{\circ}\\\Rightarrow p=216.28\approx 216.3\ \text{meters}[/tex]
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