A 16-foot ladder is leaning against a building at a 71 degree angle to the ground.
Which equation can be used to find how high the ladder reaches up the side of the building?
A) sin (71) = 16/x
B) tan (71) = 16/x
C) cos (71) = x/16
D) sin (71) = x/16

The answer to your question is the letter D.

Step-by-step explanation:

Data

length = 16 ft

angle = 71°

Opposite side = ?

Process

1.- To answer this question use trigonometric functions.

The trigonometric function that relates the Opposite side and the hypotenuse is sine.

2.- Write the trigonometric function

      sin Ф = Opposite side / hypotenuse

3.- Substitution and result

      sin (71) = x / 16

D) sin (71) = x/16

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine how high the ladder reaches up the side of the building x, we would apply the Sine trigonometric ratio.

Sin θ, = opposite side/hypotenuse. Therefore, the equation that can be used is

Sin 71 = x/16

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2