Question

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.

Answer 1

• 15 m

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