Find Side BC in Right Triangle: Given Sides 2 and 7

Question

Look at the triangle in the diagram. How long is side BC?

00:00 Find BC

00:03 Use the Pythagorean theorem in a right triangle

00:10 Substitute appropriate values and solve for BC

00:19 Isolate CB

00:22 Extract the root

00:31 Factor 45 into 9 and 5

00:37 And this is the solution to the question

To solve the exercise, it is necessary to know the Pythagorean Theorem:

A²+B²=C²

We replace the known data:

2²+B²=7²

4+B²=49

We input into the formula:

B²=49-4

B²=45

We find the root

B=√45

This is the solution. However, we can simplify the root a bit more.

First, let's break it down into prime numbers:

B=√(9*5)

We use the property of roots in multiplication:

B=√9*√5

B=3√5

This is the solution!

$3\sqrt{5}$ cm