Question

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º.
Scarlett's height is 1.65 meters, how tall is the dam?

Answer 1

Answer:

45.55 meters

Step-by-step explanation:

I'm guessing she recorded above her height, right?

To find the height of the dam, use the tangent ratio:

$tangentX=\frac{opposite}{adjacent}$

The height of the dam is the side opposite the given angle, and this will represent x. The adjacent side (the hypotenuse is NEVER considered the adjacent side) is the distance from Scarlett to the dam. The angle of elevation is the angle of 26°. Insert the values:

$tan26=\frac{x}{90}$

Solve for x. Multiply both sides by 90:

$90*(tan26)=90*(\frac{x}{90})\\\\90*tan26=x$

Insert equation into a calculator:

$x=90*tan26\\\\x=43.9$

Now add Scarlett's height:

$43.9+1.65=45.55$

The dam is 45.55 meters tall.

Finito :D