Question

At a certain time of the day, a shadow cast by John and the shadow cast by a tree end at the same point. John is 5 feet, and he is 20 feet from the tree. The two shadows end at a point that is 35 feet from the base of the tree. What is the height, in feet, of the tree? Round your answer to 1 decimal place.

a) 11.7
b) 2.1
c) 105
d) 8.75

Answer 1

By setting up a proportion using the properties of similar triangles, we calculated that the height of the tree is 11.7 feet after rounding to one decimal place, making the correct answer (a) 11.7 feet.

Step-by-step explanation:

To determine the height of the tree, we can use the properties of similar triangles. Since the shadows of John and the tree end at the same point, we can set up a proportion comparing the height and shadow lengths of John and the tree.

Let h be the height of the tree. The shadow of the tree is 35 feet long, and John, who is 5 feet tall, casts a shadow that is 35 - 20 = 15 feet long. Therefore, we have the following proportion:

John's height / John's shadow length = Tree's height / Tree's shadow length
5 feet / 15 feet = h / 35 feet

Solving for h, we get:

h = (5 feet / 15 feet) × 35 feet = (1 / 3) × 35 feet = 11.6666... feet

When rounded to one decimal place, the height of the tree is 11.7 feet.

Thus, the correct answer is (a) 11.7 feet.