Part of a road that is 452 meters in length has a slight incline. The vertical rise is 12 meters. Find the angle of elevation.
can anybody help? and it must be rounded to the nearest tenth
θ is the angle that has
sinθ = 12/452
thanks. steve
To find the angle of elevation, you can use trigonometry. Specifically, you can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the angle. Here's how you can solve this problem step by step:
Step 1: Draw a diagram
It's helpful to have a visual representation of the problem. Draw a right triangle with a horizontal base representing the road and a vertical side representing the vertical rise. Label the length of the base as 452 meters and the height as 12 meters.
Step 2: Identify the sides of the triangle
In the right triangle, the base is the adjacent side (A), the vertical rise is the opposite side (O), and the hypotenuse is the longest side (H).
Step 3: Use the tangent function
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, you want to find the angle of elevation, so you need to find the inverse tangent (also called arctan) of the ratio of the opposite side to the adjacent side.
Step 4: Calculate the angle of elevation
Using a calculator with a tangent function, divide the vertical rise (12 meters) by the length of the road (452 meters) and take the inverse tangent of the result:
angle = arctan(O/A) = arctan(12/452)
Enter this expression into a calculator:
angle ≈ 1.51 degrees
Therefore, the angle of elevation is approximately 1.5 degrees when rounded to the nearest tenth.