Question

Learning Goal:

To use trigonometric functions to find sides and angles of right triangles.

The functions sine, cosine, and tangent are called trigonometric functions (often shortened to "trig functions"). Trigonometric just means "measuring triangles." These functions are called trigonometric because they are used to find the lengths of sides or the measures of angles for right triangles. They can be used, with some effort, to find measures of any triangle, but in this problem we will focus on right triangles. Right triangles are by far the most commonly used triangles in physics, and they are particularly easy to measure.

You need to set up another simple ramp using the board from Part A (i.e., a board of length 1.56 m ). (Figure 3) If the ramp must be at a 25 ^{a} angle above the ground, how far back from the bed of the truck should the board touch the ground? Assume this is a different truck than the one from Part A.

Express your answer in meters to three significant figures.

The third frequently used trig function is the tangent function. The tangent of an angle θ is defined by the equation

tan (θ)=O/A .

This equation can be rearranged the same way that the equations for sine and cosine were rearranged previously. With the tangent of an angle, you can find the length of the adjacent side from the length of the opposite side or vice versa.

 Part C

Surveyors frequently use trig functions. Suppose that you measure the angle from your position to the top of a mountain to be 2.50°, (Figure 4) If the mountain is 1.00 km higher in elevation than your position, how far away is the mountain?

Express your answer in kilometers to three significant figures.

Answer 1

let distance from foot of mountain be x

tan 2.5 = 1/x

x = 1/ tan2.5

x = 1/ 0.04366

x = 22.9 km

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