Question

Adrian is standing on the ground 12 ft from the base of a tree that is 5 ft tall. sofi is standing on the ground 8 ft closer to the base of the tree than adrian. what’s the distance from adrian’s location on the ground to the top of the tree? what’s the distance from sofi’s location on the ground to the top of the tree?

Answer 1

The distance from Adrian's location on the ground to the top of the tree is 13 ft, and the distance from Sofi's location on the ground to the top of the tree is approximately 6.4 ft.

Step-by-step explanation:

To find the distance from Adrian's location on the ground to the top of the tree, we can use the Pythagorean theorem. The horizontal distance from Adrian's location to the base of the tree is 12 ft, and the vertical distance from the base of the tree to the top is 5 ft.

Using the theorem, we have:

c^2 = a^2 + b^2
c^2 = 12^2 + 5^2
c^2 = 144 + 25
c^2 = 169

Therefore, c = 13.

So, the distance from Adrian's location to the top of the tree is 13 ft.

To find the distance from Sofi's location on the ground to the top of the tree, we can use the same method. Since Sofi is standing 8 ft closer to the base of the tree than Adrian, her horizontal distance to the base of the tree is 4 ft.

Again, using the theorem, we have:

c^2 = a^2 + b^2
c^2 = 4^2 + 5^2
c^2 = 16 + 25
c^2 = 41

Therefore, c ≈ 6.4.

So, the distance from Sofi's location to the top of the tree is approximately 6.4 ft.

Answer 2

You have 2 right triangles here: the one created by Adrian and the one by Sofie. Let's do Adrian's first. If he is standing 12 feet from the the tree, that is the base leg of the triangle, and the vertical leg is the 5 foot tall tree. We need to find the other base angle in order to work this problem. Tan A = 5/12; tanA = .41666666; tan^-1(.416666)=22.6 degrees. Now use this degree measure and the sin ratio to find the length of the hypotenuse. sin(22.6)=5/x; x=5/sin(22.6); x=13.01. Do the same exact procedure for Sofie. Her base leg is 4 though. Tan A=5/4; tan A=1.25; tan^-1(1.25)=51.34. Now use the sin ratio to find the length of the hypotenuse. sin(51.34) = 5/x; x = 5/sin(51.34); x=6.4