What is the height of a pole standing 20 feet from the base of pole and measure the angle of the elevation to the top of the pole to be 54 degrees what's the height of the pole
This is a tangent problem
Tan(54 deg) = h/20
Once you find the Tan(54 deg) multiply by 20 to get the height.
Use a table or your calculator to find Tan (54)
To find the height of the pole, you can use trigonometry and specifically the tangent function. Here's how you can do it step by step:
Step 1: Draw a diagram representing the situation. You have a right triangle formed by the pole, the ground, and the line of sight from the ground to the top of the pole. The angle of elevation is the angle between the line of sight and the ground.
Step 2: Label the relevant parts of the diagram. Let the height of the pole be denoted as 'h' and the distance from the base of the pole to the observer be denoted as 'd'. In this case, 'h' represents the unknown value we want to find, and 'd' is given as 20 feet.
Step 3: Apply the tangent function. The tangent function, abbreviated as tan, relates the angle of elevation to the sides of a right triangle. It is defined as the ratio of the length of the side opposite the angle divided by the length of the side adjacent to the angle. In this case, tan(54 degrees) = h / d.
Step 4: Solve for the height of the pole. Rearranging the equation, we have h = d * tan(54 degrees). Substitute the given value of d as 20 feet and calculate tan(54 degrees) using a calculator. Multiply the result by 20 to obtain the height of the pole.
By following these steps, you should be able to determine the height of the pole.