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The two men measure the angle of elevation to the highest point on the rock to be 22.6°. They
then walk 17 meters closer and measured the angle of elevation to be 38.3°. To the nearest meter,
how tall is Wave Rock?
You may not use Law or Sines to solve the problem.

Sagot :

Mhanifaidn

Answer:

  • 15 m

Step-by-step explanation:

Refer to attached picture

  • The height  = h
  • Angles of elevation 22.6° and 38.3°
  • Closer distance  = d

Use tangent to solve

  • tan 22.6° = h/(d + 17) ⇒ h = (d + 17) tan 22.6° ⇒ h = 0.42(d + 17)
  • tan 38.3° = h/d          ⇒ h = d tan 38.3°           ⇒ h = 0.79d

Compare the equations above and find the value of d:

  • 0.42(d + 17) = 0.79d
  • 0.42d + 7.14 = 0.79d
  • 0.79d - 0.42d = 7.14
  • 0.37 d = 7.14
  • d = 7.14/0.37
  • d = 19.3 m

Now find the value of h:

  • h = 0.79d
  • h = 0.79*19.3
  • h = 15

Wave Rock is 15 m tall

View image Mhanifa
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