Question

Use the triangle at the right. Find the length of the missing side.
1. a = 16, b = 63 2. b = 2.1, c = 2.9

Answer 1

Since this is a right triangle, the Pythagorean theorem applies, which states:

\[a^{2} + b^{2} = c^{2}\]

So, for the first problem:

\[c = \sqrt{16^{2} + 63^{2}}\]

Answer 2

1.79
2.5

Answer 3

Ok so what'sthe second one?

Answer 4

how did you get the first one? can you show me?

Answer 5

10

Answer 6

The second problem is slightly more complicated. Rewrite the equation so that "a" is on the left side by itself:

\[a^{2} = c^{2} - b^{2}\]

Then take the square root of both sides:

\[a = \sqrt{ c^{2} - b^{2}}\]

Now insert the values for "b" and "c" that you were given:

\[a = \sqrt{ (2.9)^{2} - (2.1)^{2}}\]

Answer 7

I apologize for skipping steps in the first problem. Here are all of the steps for soling the first problem.

\[a^{2} + b^{2} = c^{2}\]
Moving "c" to the left side of the equation:
\[c^{2} = a^{2} + b^{2}\]
Squaring both sides:
\[c = \sqrt{a^{2} + b^{2}}\]
Substituting the given values:
\[c = \sqrt{16^{2} + 63^{2}}\]

Hope this helps.

Answer 8

Just noticed there is one more step I made implicitly. The following are true:

\[\sqrt{a^{2}} = a\]
\[\sqrt{c^{2}} = c\]