A tree casts a shadow that is 20 ft long. The angle of elevation of the sun is 29°. How tall is the tree?

You can use the trig ratios. Draw a diagram to see which one is appropriate. Tan would be used. Tan29=x/20 20Tan29=x Put this into your calculator and see what you get

Answered by madison12340 | 2024-06-10

By using the tangent of the angle of elevation of the sun (29 degrees) and the length of the tree's shadow (20 feet), the height of the tree is calculated to be approximately 11.086 feet.
To determine the height of the tree given the length of its shadow and the angle of elevation of the sun, we can use trigonometric functions. Specifically, we would use the tangent function which is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this scenario, the height of the tree is the opposite side, and the length of the shadow is the adjacent side. Using the formula tan(\theta) = opposite/adjacent, where θ is the angle of elevation, we get:
tan(29\degree) = tree height / 20 ft
The tangent of 29 degrees can be found using a scientific calculator or a trigonometry table. Assuming tan(29\degree) = 0.5543 (rounded to four decimal places), we can solve for the tree height as follows:
0.5543 = tree height / 20 ft
tree height = 0.5543 * 20 ft
tree height = 11.086 ft
Therefore, the tree's height is approximately 11.086 feet.

Answered by BenicioBrody | 2024-06-24

The height of the tree can be calculated using the tangent of the angle of elevation of the sun and the length of the shadow. Using the formula h = s × tan ( θ ) , the tree's height is determined to be approximately 11.086 feet. This is done by substituting the values into the formula and solving for height.
;

Answered by BenicioBrody | 2024-11-20