Question
A 13 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 5 feet from the base of the tree. The base of the tree and the ground form a right angle as shown. What is the distance , in feet, between the ground and the top of the ladder? Round your answer to the nearest tenth.
Answer
4.4
(158 Votes)
Owen
Master · Tutor for 5 years
Answer
To find the distance between the ground and the top of the ladder, we need to determine the height at which the ladder touches the tree. Since the ladder, the ground, and the height of the tree form a right-angled triangle, we can use the Pythagorean theorem to solve for the height.The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):c² = a² + b²Here, the length of the ladder is the hypotenuse (c = 13 ft), and the distance from the base of the tree to the ladder is one of the other sides (a = 5 ft). We need to find the height of the tree, which is the other side (b).Let's plug in the values we have:13² = 5² + b²169 = 25 + b²169 - 25 = b²144 = b²Now, we take the square root of both sides to solve for b:√144 = b12 = bSo, the height of the tree, or the distance between the ground and the top of the ladder, is 12 feet. Since the question asks for the answer to the nearest tenth, the final answer is:12.0 feet.