at a point 27 m from the front of a pole, the angle of elevation of the top of the pole is 53. find the height of the pole

tan 53 = h/27

To find the height of the pole, we can use trigonometry. Here's how you can solve this problem step by step:

Step 1: Draw a diagram: Start by drawing a diagram to visualize the problem. Draw a vertical line to represent the pole, and label it as "P". Mark a point 27 m away from the front of the pole, and label it as "A". Also, mark the angle of elevation, which is 53 degrees.

Step 2: Identify the relevant trigonometric ratio: In this problem, we are given the opposite side (height of the pole) and the adjacent side (distance from the pole to the point of observation). So, we can use the tangent ratio, which is defined as "opposite/adjacent". In this case, the tangent of the angle of elevation is equal to the height of the pole divided by the distance from the pole to the point of observation.

Step 3: Set up the equation: Let's denote the height of the pole as "h". According to the tangent ratio, we have:

tan(53°) = h/27

Step 4: Solve the equation: Now, we can solve the equation for "h". Multiply both sides of the equation by 27:

27 * tan(53°) = h

Using a scientific calculator, find the tangent of 53 degrees and multiply it by 27 to get the value of "h".

Step 5: Calculate the height: After substituting the value of the tangent of 53 degrees and multiplying it by 27, you will get the height of the pole in meters.

Following these steps, you should be able to find the height of the pole.