Math, asked by 05hemantbhati, 10 months ago

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?

Answers

Answered by knjroopa
2

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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