Question

Use the information in the diagram to determine the height of the tree to the nearest foot.

Answer 1

C.) 80 ft

Explanation:

Using the diagram, the little lines that intersect the sides of the triangle tell us that those lengths are equal. When you see a single line, any other side length that has a single line is the same value.

We'll call our unknown side length, the height of the tree, a, while the height of the building will be A. And we'll label the other two given side lengths b and c.

We know that:

• A = 160 ft
• b = 120
• c = 144

So the entire base, C, must be 2(144) and the entire hypotenuse, B, must be 2(120).

Basically, the values of the triangle are doubled. So using this information, we can determine that the height of the tree, a, must be 160/2. Which is 80.

(This is a little confusing, sorry!)

You can check your work by making a proportion:

288/2 = 144/1

240/2 = 120/1

so:

160/2 = x/1

Solve the proportion by solving for x.

Cross multiply, then solve for x and you'll find that x = 80.

Answer 2

80 feet is the height of the tree.

Explanation:

The image shows a similarity between triangles.

Notice that the building forms a right triangle and the tree enclosed a smaller right triangle.

The hypothenuse of the smaller triangle is 144 feet, while the height of the bigger triangle is 160 feet. Additionally, the hypothenuse of the bigger triangle is 288 feet.

Based on all those given elements, we can form the proportion

`(288)/(144)=(160)/(y)`

Where
`y` is the height of the tree

`2=(160)/(y) \\y=(160)/(2)\\ y=80`

Therefore, the height of the tree is 80 feet.