Question

A 12-foot support wire is attached to the top of a pole shown. The wire is anchored in the ground 4-feet from the pole.


Which equation can be used to find y, the height if the pole in feet?

A. y = 12 + 4

B. 12 = y + 4

C. y^2 = 12^2 + 4^2

D. 12^2 = y^2 + 4^2

It is not C.

Answer 1

Equation D. $12^{2} = y^{2} + 4^{2}$ can be used to solve y in feet.

Step-by-step explanation:

Step 1:

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The hypotenuse is the side opposite the right angle. So the hypotenuse of this given triangle is 12 feet.

The other two sides of the triangle are 4 feet long and y feet long.

Step 2:

Substituting the values we know in the Pythagorean theorem, we get

$12^{2} =4^{2} + y^{2},$ which can also be written as

$12^{2} = y^{2} + 4^{2} .$

This is option D.