Question

the angel of elevation from where casey is standing to the top of an 84ft tall lighthouse is 58 degrees how far is casey standing from the lighthouse

Answer 1

Answer: 52.489…

Step-by-step explanation:

Angle of elevation is 58 degrees, and the opposite value is 84 feet, so you’re lookin g for adjacent. That means you’ll use tangent to solve this equation:

Tan(58)=84/x

Answer 2

Answer: Casey is standing 52.5 feet from the lighthouse.

Step-by-step explanation:

A right angle triangle is formed. The height of the lighthouse represents the opposite side of the right angle triangle. The distance, h from the lighthouse to where Casey is standing represents the adjacent side of the right angle triangle. Casey's line of sight along the angle of elevation represents the hypotenuse.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan 58 = 84/h

h = 84/tan 58 = 84/1.6

h = 52.5 feet