Finding the Distance from a Coordinate Grid

Question

A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented on an x-axis and the base of the house is at the origin. There are two trees on the property. One tree is 10 feet from the base of the house and is 12 feet tall. The other tree is 14 feet from the base of the house and is 8 feet tall. What is the distance from the base of the house to the closest treetop? Round your answer to the nearest tenth.

Answer 1

draw a diagram

you have 2 right triangles

find the hypotenuse of each; these will be the distances you want

d^2=10^2+12^2

d^2=244

d=√244

d=15.6 feet (closest)

d^2=14^2+8^2

d^2=196+64

d^2=260

d=√260

d=16.1 feet