Question

How do you use the Pythagorean Theorem to solve for the missing side given a = 7, c = 21?

Answer 1

Hint: In this problem we have to use the Pythagorean Theorem to find the missing side of the right triangle with the given measures where we can assume c as the hypotenuse and we have a = 7, c = 21. We know that the Pythagoras Theorem is $$a^2+b^2=c^2$$. We can see that, we are already given the value for a and c, which we can substitute in the formula where the missing side is b, which we have to find.

Complete step by step solution:
We know that we have used the Pythagorean Theorem to find the missing side of the right triangle with the given measures given c is the hypotenuse and we have a = 7, c = 21.

We know that the Pythagoras Theorem is $$a^2+b^2=c^2$$.
We can substitute the value a = 7, c = 21 in the above formula, we get
$$\Rightarrow 7^2+b^2={21}^2$$
We can now simplify the above step, we get
$$\begin{array}{rl}& \Rightarrow b^2=441-49\\ & \Rightarrow b^2=392\end{array}$$
We can now take square root on both sides, we get
$$\Rightarrow b=\sqrt{392}=19.79$$
Therefore, the missing side of the given right triangle is $$\sqrt{392}$$units.

Note: Students should remember the Pythagoras theorem formula is $$a^2+b^2=c^2$$. Where the sum of squares of two sides is equal to the square of the hypotenuse. We should also see that the given triangle should be a right-angle triangle, where Pythagora's theorem is only applied to right-angled triangles.