Question

Can someone please help me?
Find the value of x.

Answer 1

It's been a long time, I really don't remember how to do this. Can somebody walk me through?

Answer 2

are you familiar with the trigonometric functions?

Answer 3

You can also use the ratios of the lengths of the sides of a 45-45-90 triangle.

Answer 4

Also, Pythagoras theorem.

Answer 5

you can use the Cos formula
Cos = Adjacent/hypotenuse
Cos 45 = 12/x
Solve for x and thats all

Answer 6

@mathstudent55 let me know of that method because I haven't really learned about the trig functions yet.

Answer 7

What is angle measure a?

Answer 8

45 degrees

Answer 9

Let's use the Pythagoras theorem

\(a^2 + b^2 = c^2\)

You know one angle is a right angle with measure 90 deg.
The other given angle has measure 45 deg.
What is the measure of the third angle?

Answer 10

Good. In a triangle, if 2 angles are congruent, then the sides opposite those angles are congruent.

Answer 11

\[\cos 45 = \frac{ 12 }{ x }\]
Cross multiply
\[12 = \cos 45 * x\]
divide both sides by cos 45
\[12\sqrt{2} = x\]

Answer 12

What is side length b?

Answer 13

So that should be 12 too, right?

Answer 14

Correct.

Answer 15

Oh so than I can use pythagorean theorem to solve for c now.

Answer 16

Now we can use the Pythagoras theorem with legs of length 12 and unknown hypotenuse.
The legs are a and b. The hypotenuse is c.

\(a^2 + b^2 = c^2\)

\(12^2 + 12^2 = c^2\)

Can you solve for c?

Answer 17

That's also a good way

Answer 18

I got an unending decimal, but I rounded it to 16.97

Answer 19

or you can keep it as \[12\sqrt{2}\]

Answer 20

Oh yeah, that's right. Thanks:)

Answer 21

yw:)

Answer 22

These problems should be answered with a number in radical form. This way the answer is exact.

\(12^2 + 12^2 = c^2\)

\(144 + 144 = c^2\)

\(c^2 = 288\)

\(c = \sqrt{288} \)

\(c = \sqrt {144 \times 2}\)

\(c = \sqrt{144} \times \sqrt 2\)

\(c = 12\sqrt 2\)

In this problem the hypotenuse is labeled x, so the answer is:

\(x = 12\sqrt{2}\)

Answer 23

You are correct.