To determine the length of each light string, we can use the sine ratio from trigonometry. The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse.
In this case:
- The height of the pole (the opposite side) is 7 feet.
- Let's denote the length of the light string (the hypotenuse) as \( L \).
- The angle with the ground is \( 73.5^\circ \).
The sine function can be expressed as: \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] Substituting the known values: \[ \sin(73.5^\circ) = \frac{7}{L} \]
To find \( L \): \[ L = \frac{7}{\sin(73.5^\circ)} \]
Now, we calculate \( \sin(73.5^\circ) \):
Using a calculator: \[ \sin(73.5^\circ) \approx 0.9563 \]
Now plug this value into the equation for \( L \): \[ L = \frac{7}{0.9563} \approx 7.33 \]
Rounding to the nearest tenth gives: \[ L \approx 7.3 \text{ feet} \]
Therefore, the length of each light string must be approximately 7.3 feet.
1 answer