A 10-foot pole is supporting a tent and has a rope attached to the top. The rope is pulled straight and the other end is attached to a peg two foot above the ground. The rope and the pole form an angle that measures 40, as shown below.
The pole, the rope, and an imaginary line that runs across the ground from the top of the peg to the pole form a right triangle. The hypotenuse is unknown. The pole is adjacent to the 40-degree angle, and it is labeled 10 feet. The 10 foot measurement includes the height of the 2 foot peg. The imaginary line that runs across the ground is opposite the 40-degree angle, and it is not labeled.
Which expression shows the length of the rope?
The length of the rope can be found using trigonometry. In this case, we can use the sine function since the opposite side and the hypotenuse are involved.
sin(40°) = opposite/hypotenuse
sin(40°) = x/10
To find the length of the rope (x), we can rearrange the equation:
x = 10 * sin(40°)
Therefore, the expression to show the length of the rope is:
x = 10 * sin(40°)