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?

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