A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by the 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.
Use the Pythagorean Theorem for each tree with the distance from the house to the tree being one side of a right triangle (side a) and the height of the tree being the other side (side be). You need to calculate the hypotenuse (side c)
For the first tree: a = 10 b = 12 c2 = a2 + b2 ---> c2 = 102 + 122 ---> c = 15.6 feet
For the second tree: a = 14 b = 8 c2 = a2 + b2 ---> c2 = 142 + 82 ---> c = 16.1 feet