Question

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

Answer 1

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