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beks73 [17]
2 years ago
8

The two men measure the angle of elevation to the highest point on the rock to be 22.6°. They

Mathematics
1 answer:
IgorC [24]2 years ago
3 0

Answer:

  • 15 m

Step-by-step explanation:

<em>Refer to attached picture</em>

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

<u>Use tangent to solve</u>

  • 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

<u>Compare the equations above and find the value of d:</u>

  • 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

<u>Now find the value of h:</u>

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

Wave Rock is 15 m tall

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