Question

Please help ASAP!!! You are standing 15 feet from a tree. Your line of sight from the top of the tree to the bottom of the tree forms a 90 degree angle. The distance between your line of sight and the ground is 5 feet. Estimate the height of the tree.

Answer 1

To estimate the height of the tree, use similar triangles and set up a proportion to solve for the tree height.

Step-by-step explanation:

To estimate the height of the tree, we can use similar triangles. Draw a diagram to represent the situation. Let the height of the tree be 'h'. From the information given, we can form two similar triangles: one with the tree and your line of sight, and the other with the tree, your line of sight, and the distance between your line of sight and the ground. Set up the proportion:

tree height / distance between your line of sight and the ground = distance between you and the tree / distance between you and your line of sight

Using this proportion, we can solve for the height of the tree:

h / 5 = 15 / (15 + 5)

h / 5 = 15 / 20

h = 5 * (15 / 20)

h = 3.75 feet

Answer 2

Estimate tree height: 50 ft

First, you'd have to get the hypotenuse of the smaller triangle to get the base of the bigger triangle. This can easily be done using Pythagorean theorem (15^2 + 5^2 = hyp^2). The hyp of smaller triangle/base of bigger triangle is 15.81 ft. Then you'd also want to get the angle adjacent to the 5 ft leg, and opposite the 15 ft leg of the smaller triangle to get one of the two remaining angles of the bigger triangle. This can be done via sohcahtoa, using the TOA part. The inverse tangent of opposite/adj leg will give you the angle you're looking for (71.6 deg). With that, you'll know that the remaining angle is 18.4 deg (sum of all angles is 180). You can solve for the height of the tree/hypotenuse of the bigger triangle by using SOH. Sine of 18.4 is equal to 15.81/hypotenuse. Solving for that will give you around 50 ft.