a pine tree casts a shadow that is 7.9 feet long when the sun is 80 degrees above the horizon

find the height of the tree

hint:

looks like a tangent set-up

knj

To find the height of the tree, we can use trigonometry. The length of the shadow and the angle between the sun and the ground can help us determine the height of the tree.

1. Begin by drawing a diagram representing the situation. The vertical line represents the tree, and the horizontal line represents the ground. The length of the shadow (7.9 feet) is shown.

|
Tree |
|
|
----------------------
Shadow (7.9 ft)

2. The angle formed between the ground and the sun's rays is given as 80 degrees.

3. Now, we can use the tangent function (tan) to find the height of the tree. The tangent of an angle is equal to the opposite side (height of the tree) divided by the adjacent side (length of the shadow).

tan(angle) = height of tree / length of shadow

tan(80 degrees) = height of tree / 7.9 feet

4. To find the height of the tree, multiply both sides of the equation by the length of the shadow.

height of tree = tan(80 degrees) * 7.9 feet

5. Calculating the height using a scientific calculator:

height of tree = tan(80 degrees) * 7.9 feet = 16.08 feet

Therefore, the height of the pine tree is approximately 16.08 feet.