Question

Question Trey wants to use string lights to build a flagpole lighted tree in his front yard. Trey already had a 7 ft tall pole mounted in the ground. If the angle each light string makes with the ground is 73.5°, use the sine ratio to determine how long each light string must be to reach the top of the pole. Round your answer to the nearest tenth.(1 point) Responses 6.7 feet 6.7 feet 23.6 feet 23.6 feet 2 feet 2 feet 7.3 feet 7.3 feet

Answer 1

To determine the length of each light string (hypotenuse) necessary to reach the top of a 7 ft tall pole using the sine ratio, we can use the following relationship from trigonometry:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

Here:
- \(\theta\) is the angle the light string makes with the ground (73.5°),
- the opposite side is the height of the pole (7 ft),
- and the hypotenuse is the length of the string light (which we want to find).

Rearranging the formula to find the hypotenuse, we have:

\[
\text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)}
\]

Now substituting the known values:

\[
\text{hypotenuse} = \frac{7 \text{ ft}}{\sin(73.5^\circ)}
\]

Calculating \(\sin(73.5^\circ)\):

\[
\sin(73.5^\circ) \approx 0.9563
\]

Now substitute this back into the equation:

\[
\text{hypotenuse} = \frac{7}{0.9563} \approx 7.3 \text{ ft}
\]

Thus, the length of each light string must be approximately \(7.3\) feet when rounded to the nearest tenth.

The correct response is **7.3 feet**.