Question

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

Answer 1

Answer:

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

Step-by-step 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.

$\sqrt{b^2}=\sqrt{64$

$b=\sqrt{64}$

$b=8$

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