Jessica sets up a volleyball net in her backyard. To secure the net in place, she extends a rope from the top of each of the two poles at a diagonal to the ground. Once the poles are placed in the ground, they are 7 feet tall; the rope she uses is 9 feet long. Using the inverse of sine, what is the approximate angle formed between the ground and the rope?(1 point) Responses 45° 45° 51° 51° 39° 39° 90°
51°
To find the angle, we can use the inverse sine function.
Let's label the triangle formed by the ground, the rope, and the pole as follows:
- The side opposite the angle we want to find is 7 feet (height of the pole).
- The hypotenuse is 9 feet (the length of the rope).
- The angle we want to find is labeled as θ.
Using the sine function, we have sin(θ) = opposite/hypotenuse
sin(θ) = 7/9
To find the angle θ, we take the inverse sine (sin^-1) of both sides:
θ = sin^-1(7/9)
θ ≈ 51°
Therefore, the approximate angle formed between the ground and the rope is 51°.