on a sunny day, the sun ray meet the ground at an angle of 35 degrees. a pole casts a shadow 21.3m in length. how tall is the pole.
It helps if you draw it out.Anyways
Let H be the height of the pole.
Tan35=H/21.3
Solve for H
To find the height of the pole, we can use basic trigonometry. Here's how you can solve it step by step:
1. Draw a diagram: Draw a straight line representing the pole, and draw another line coming from the top of the pole to the ground, representing the sun rays.
2. Identify the angles: The angle between the sun rays and the ground is given as 35 degrees.
3. Identify the known values: The length of the shadow cast by the pole is given as 21.3m.
4. Determine the trigonometric ratio to use: Since we are trying to find the height of the pole, we need to use the tangent function. The tangent of an angle is the ratio of the opposite side (the height of the pole) to the adjacent side (the length of the shadow).
5. Apply the tangent function: The tangent of an angle theta is equal to the opposite side divided by the adjacent side:
tan(theta) = Opposite/Adjacent
In this case, tan(35) = height of the pole / 21.3
6. Solve for the height of the pole:
height of the pole = tan(35) * 21.3
You can use a scientific calculator or online calculator to find the tangent of 35 degrees and then multiply it by 21.3 to get the height.
Following these steps, you should be able to calculate the height of the pole using trigonometry.