Question

If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70° to 60°, what is the height of the building?

Answer 1

Step-by-step explanation:

Given  

If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70° to 60°,  what is the height of the building?

• Let AB  be the building. Let h m be its height.
• Given CD = 10 m
• Let BC = x m
• In triangle ABC,
• We get tan 70 = AB/BC
•                        = h/x
• So h = x tan 70 ------------1
• Now in triangle ABD,
• We get tan 60 = AB/Bd
•                       = h/x + 10
• So h = tan 60 (x + 10)
• From 1
• x tan 70 = tan 60(x + 10)
• x(tan 70 – tan 60) = 10 tan 60
• x = 10 tan 60 / tan 70 – tan 60
• substituting in equation 1 we get
• h = 10 tan 60 / tan 70 – tan 60 x tan 70

So h = 46.87

the height of the building is 46.87 m

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