Question

The Tangent Ratio Quick Check 3 of 53 of 5 Items Question A zipline starts 120 feet above the ground and covers a diagonal distance, forming a triangle with the ground. If the angle of elevation where the zip line meets the ground is 65° , what is the horizontal distance from the base of the tower to where the zip line ends?(1 point) Responses 132 ft. 132 ft. 51 ft. 51 ft. 56 ft. 56 ft. 257 ft. 257 ft. Skip to navigation page 8 of 8

Answer 1

To find the horizontal distance from the base of the tower to where the zip line ends, we can use the tangent ratio from trigonometry. The tangent of an angle in a right triangle is defined as the opposite side divided by the adjacent side.

Here, we have:
- The height of the zipline above the ground (the opposite side) = 120 feet
- The angle of elevation = 65°

Using the tangent function:
\[
\tan(65°) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{120}{x}
\]
Where \(x\) is the horizontal distance we need to find.

Rearranging the equation to solve for \(x\):
\[
x = \frac{120}{\tan(65°)}
\]

Now, let's calculate \(\tan(65°)\) using a calculator:
\[
\tan(65°) \approx 2.1445
\]

Now substituting back:
\[
x = \frac{120}{2.1445} \approx 55.9 \text{ ft}
\]

Rounding this to the nearest whole number gives us approximately \(56\) ft.

Therefore, the answer is **56 ft**.