Answer:
2.81 feet.
Step-by-step explanation:
Please find the attachment.
We have been given that an 80-foot rope is attached to a boat 7 feet above the water level and a boy jumps over the wake while wake-boarding. We are asked to find the distance between boy's hands and the water level.
Let h represent opposite side of right triangle.
We can see that rope forms a right triangle with boat and water level, where 80 feet is hypotenuse of triangle to 87 degree angle.
The distance between boy's hands and the water level would be 7 feet minus the opposite side of right triangle.
[tex]\text{Distance between boy's hands and the water level}=7-h[/tex]
We know that cosine relates the adjacent side of right triangle with hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}(87^{\circ})=\frac{h}{80}[/tex]
[tex]\text{cos}(87^{\circ})\cdot 80=\frac{h}{80}\cdot 80[/tex]
[tex]80\cdot\text{cos}(87^{\circ})=h[/tex]
[tex]h=80\cdot 0.052335956243[/tex]
[tex]h=4.18687649944[/tex]
[tex]\text{Distance between boy's hands and the water level}=7-4.18687649944[/tex]
[tex]\text{Distance between boy's hands and the water level}=2.81312350056[/tex]
[tex]\text{Distance between boy's hands and the water level}\approx 2.81[/tex]
Therefore, the distance between boy's hands and the water level is approximately 2.81 feet.
