A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10^(@) to the horizontal. Calculate the length of the zip wire. 25.4 m 144.0m 141.8 m 24.6 m

Identify values and equation: Identify the known values and the equation to use. We know the distance between the two posts (the adjacent side of the right triangle) is 25 meters, and the angle of elevation is 10 degrees. We need to find the length of the zip wire, which is the hypotenuse of the right triangle. We will use the cosine function, which relates the adjacent side and hypotenuse of a right triangle to the angle: cos(θ) = adjacent/hypotenuse.Use cosine function: Use the cosine function to set up the equation. cos(10°) = 25 / hypotenuse We need to solve for the hypotenuse.Rearrange for hypotenuse: Rearrange the equation to solve for the hypotenuse. hypotenuse = 25 / cos(10°) Now we can calculate the length of the hypotenuse using a calculator.Calculate hypotenuse: Calculate the length of the hypotenuse using a calculator. hypotenuse ≈ 25 / cos(10°) hypotenuse ≈ 25 / 0.9848 (cosine of 10 degrees is approximately 0.9848) hypotenuse ≈ 25.4

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A zip wire runs between two posts,
25m apart. The zip wire is at an angle of
10^(@) to the horizontal. Calculate the length of the zip wire.

25.4 m

144.0m

141.8 m

24.6 m

$1$ . A zip wire runs between two posts, $25 \mathrm{~m}$ apart. The zip wire is at an angle of $10^{\circ}$ to the horizontal. Calculate the length of the zip wire. $\newline$ $25.4 m$ $\newline$ $144.0 \mathrm{~m}$ $\newline$ $141.8 m$ $\newline$ $24.6 m$

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Math Problems

Algebra 2

Pythagorean Theorem and its converse

Full solution

1

. A zip wire runs between two posts,

25 \mathrm{~m}

apart. The zip wire is at an angle of

10^{\circ}

to the horizontal. Calculate the length of the zip wire.

\newline

25.4 m

\newline

144.0 \mathrm{~m}

\newline

141.8 m

\newline

24.6 m

Identify values and equation: Identify the known values and the equation to use. $\newline$ We know the distance between the two posts (the adjacent side of the right triangle) is $25$ meters, and the angle of elevation is $10$ degrees. We need to find the length of the zip wire, which is the hypotenuse of the right triangle. $\newline$ We will use the cosine function, which relates the adjacent side and hypotenuse of a right triangle to the angle: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$ .
Use cosine function: Use the cosine function to set up the equation. $\newline$ $\cos(10^\circ) = \frac{25}{\text{hypotenuse}}$ $\newline$ We need to solve for the $\text{hypotenuse}$ .
Rearrange for hypotenuse: Rearrange the equation to solve for the hypotenuse. $\newline$ hypotenuse $= \frac{25}{\cos(10^\circ)}$ $\newline$ Now we can calculate the length of the hypotenuse using a calculator.
Calculate hypotenuse: Calculate the length of the hypotenuse using a calculator. $\newline$ hypotenuse $\approx \frac{25}{\cos(10°)}$ $\newline$ hypotenuse $\approx \frac{25}{0.9848}$ (cosine of $10$ degrees is approximately $0.9848$ ) $\newline$ hypotenuse $\approx 25.4$