A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. The pole's shadow is 16 meters long and points directly up to the slope. The angle of elevation of the sun is 20 degrees. Draw the triangle. Write an equation to solve the problem.
To solve this problem, we can draw a right triangle to represent the given information. Here's how you can draw the triangle:
1. Draw a horizontal line to represent the ground.
2. From one end of the horizontal line, draw a vertical line to represent the flagpole.
3. At the other end of the horizontal line, draw a line slanting upwards at an angle of 12 degrees to represent the slope.
4. From the top of the flagpole, draw a line directly to the slope. This line represents the shadow of the flagpole.
5. Label the point where the shadow touches the slope as point A, the top of the flagpole as point B, and the point where the slope touches the ground as point C.
Now, let's write the equation to solve the problem. We need to find the height of the flagpole (BC). Here's the equation we'll use:
tan(θ) = opposite / adjacent
In this case, we want to find the height BC, which is the opposite side, and we know the shadow length (AB), which is the adjacent side. The angle of elevation of the sun (θ) is given as 20 degrees. Therefore, we have:
tan(20°) = BC / 16 meters
By rearranging the equation, we can solve for BC:
BC = 16 meters * tan(20°)
Calculating the right-hand side of the equation will give us the height of the flagpole.