Question

Please explain to me how to do this question with right answer

Answer 1

`\boxed {\boxed {\sf b=8}}`

Explanation:

The Pythagorean Theorem is:

`a^2+b^2=c^2`

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

In this triangle, 6 and b are the legs, because they form the right angle.

10 is the hypotenuse, because it is opposite the right angle. Plus, it's the longest side.

`a=6 \\b=b\\c=10`

Substitute the values into the Theorem.

`6^2+b^2=10^2`

Evaluate the exponents.

• 6²= 6*6= 36

`36+b^2=10^2`

• 10²= 10*10= 100

`36+b^2=100`

Subtract 36 from both sides of the equation to isolate the variable (b).

`36-36+b^2=100-36`

`b^2=100-36`

`b^2=64`

b is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

`√(b^2)=\sqrt{64`

`b=√(64)`

`b=8`

In this triangle, b (the other leg) is equal to 8