when the sun is 57 degree up from the horizon,a tree cast a shadow 14 yard long.how tall is the tree?
height/14 =57 tan
To determine the height of the tree, you need to use trigonometry and the concept of similar triangles. Here are the steps to calculate the height of the tree:
1. Draw a diagram: Sketch a vertical line to represent the tree and another line to represent its shadow. Label the height of the tree (which is what we want to find) as "h" and the length of the shadow as "s."
2. Identify the angles: According to the information given, the angle of elevation of the sun's rays from the horizon is 57 degrees. We can label this angle as "θ."
3. Form a right triangle: Connect the top of the tree to the end of the shadow, creating a right triangle with the line representing the height of the tree as the vertical side (h) and the shadow as the base (s).
4. Determine the trigonometric function: Since we know the angle (57 degrees) and the length of the opposite side (h), we can use the tangent function. Tangent is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. In this case, the tangent of angle θ can be written as tan(θ) = h/s.
5. Rearrange the formula: We can rearrange the formula to solve for h. Multiply both sides of the equation by s to isolate h: h = s*tan(θ).
6. Substitute the known values: Substituting the values given in the question, h = 14 yards * tan(57°).
7. Calculate the height: Using a calculator, find the tangent of 57 degrees and multiply it by 14 yards to get the height of the tree.
By following these steps, you can determine the height of the tree based on the given information.