Question

Find the value of in the triangle shown below.

Answer 1

x=6

Explanation:

This is a right triangle, because of the little square in the corner. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

Where a and b are the legs and c is the hypotenuse.

In this triangle, we know that 2.5 and x are the legs, because they form the right angle. We know that 6.5 is the hypotenuse, because it is opposite the right angle.

Therefore, 2.5 and x are a and b, and 6.5 is c.

2.5^2+x^2=6.5^2

Evaluate the exponents

6.25+x^2=42.25

Since we are trying to find x, we have to get x by itself. First, subtract 6.25 from both sides

6.25-6.25+x^2=42.25-6.25

x^2=36

Next, take the square root of both sides, because x is being squared.

`√(x^2)=\sqrt{36`

x=6

Answer 2

x= 6

Explanation:

We can use the Pythagorean theorem to find x

x^2 + 2.5^2 = 6.5 ^2

x^2+ 6.25 =42.25

Subtract 6.25 from each side

x^2+ 6.25-6.25 =42.25-6.25

x^2 =36

Take the square root of each side

x = sqrt(36)

x= 6