Question

A 13-foot ladder is leaning against a tree. The bottom of the ladder is 5 feet away from the bottom of the tree. Approximately how high up the tree does the top of the ladder reach?

Answer 1

Answer:

12 feet

Step-by-step explanation:

It's a classic 5-12-13 triangle or you can used the Pythagorean Theorem:

$13^{2} -5^{2}=x^{2} \\169-25=x^{2} \\144=x^{2} \\12=x$

Answer 2

Answer:

The tree is 12 about feet high.

Step-by-step explanation:

The way to find the answer is with Pythagorean Theorem.

The ladder is 13 feet and is the hypotenuse or c.

13^2

The 5 feet away from the tree is one of the two legs or a

5^2

We are trying to find the second leg, b.

b^2

Now you write the formula:

c^2=a^2+b^2

Then insert the numbers:

13^2=5^2+b^2

The isolate the variable:

Subtract 5^2 on each side

13^2 - 5^2=b^2

Now flip the expression so the variable is on the left side:

b^2=13^2 - 5^2

Simplify:

b^2=169 - 25

Simplify:

b^2= 144

Square root both sides to get the variable alone:

srt b^2 is b

srt 144 is 12

b=12

Don't forget units!

The tree is 12 feet high