Question

A tree casts a shadow that is 150 feet long. If the angle of elevation from the tip of the shadow to the top of the tree is 30°, how tall is the tree to the nearest foot?

Answer 1

To find the height of the tree, use trigonometry with the tangent function. Set up the equation tan(30°) = h/150 and solve for 'h'. The height of the tree is approximately 86.6 feet.

Step-by-step explanation:

To find the height of the tree, we can use trigonometry. We have an angle of elevation of 30° and the length of the tree's shadow, which is 150 feet. Let's call the height of the tree 'h'. Using the tangent function, we can set up the equation tan(30°) = h/150

. Solving for 'h', we have h = 150 * tan(30°). Using a calculator, we find the height of the tree to be approximately 86.6 feet.