You are flying a kite while standing 80 ft from a fence. If the kite string makes a 50° angle with
the ground, how much string, in feet, is let out
when the kite is directly above the fence?

124.5 ft

Step-by-step explanation:

Draw a figure. It is a triangle.

Kite

B  | \

   |       \

   |              \

   |                    \      string

   |                           \

   |                                \

   |                                       \

   |                                            \

   | __                            50 deg    \

C  |----|----------------------------------------   A

 fence                80 ft                  you are here

You are at point A. The kite is at point B. The fence is at point C. Angle C is a right angle.

The length of the string is the hypotenuse of the triangle, side AB. The bottom side of the triangle, side AC, the ground, is the adjacent leg for angle A.

The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

124.5 ft

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions