Math

QuestionA train track rises at 1010^{\circ}. How high does it rise over 230 feet? Estimate to two decimal places. A. 121.34 in B. 45.85 ft C. 40.56 ft D. 115.36 in E. None.

Studdy Solution

STEP 1

Assumptions1. The train track slopes upward at an angle of 1010^{\circ} . The horizontal distance of the track is230 feet3. We are asked to find the vertical rise of the track4. We will use the trigonometric function tangent, which is defined as the ratio of the opposite side (rise) to the adjacent side (run) in a right triangle

STEP 2

We can use the tangent of the slope angle to find the rise of the track. The formula is as followstan(θ)=riserun\tan(\theta) = \frac{rise}{run}

STEP 3

We are given the run (horizontal distance) and the angle, so we can rearrange the formula to solve for the riserise=tan(θ)×runrise = \tan(\theta) \times run

STEP 4

Now, plug in the given values for the angle and the run to calculate the rise.
rise=tan(10)×230feetrise = \tan(10^{\circ}) \times230\, feet

STEP 5

First, we need to calculate the tangent of 1010^{\circ}.

STEP 6

Use a calculator to find the tangent of 1010^{\circ}. Ensure your calculator is in degree mode.
tan(10)0.1763\tan(10^{\circ}) \approx0.1763

STEP 7

Now, multiply the tangent of 1010^{\circ} by the run to find the rise.
rise=0.1763×230feetrise =0.1763 \times230\, feet

STEP 8

Calculate the rise.
rise0.1763×230feet=40.55feetrise \approx0.1763 \times230\, feet =40.55\, feetThe rise of the track over a horizontal distance of230 feet is approximately40.55 feet. Rounding to two decimal places, the rise is40.55 feet. So, the correct answer is C.40.56 feet.

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