Question

What is the length of the hypotenuse?

(Picture below.)

Answer 1

Use what i just taught you to find the opposite side length. Then use the Pythagorean theorem.

Answer 2

\[\cos \theta=\frac{\text{adjacent side}}{\text{hypotenuse}}\]

Answer 3

Tan = 45?

Answer 4

Ohh

Answer 5

we have an angle, an an adjacent side length, we are solving for the hypotenuse

Answer 6

Or you can do it Unkles way but i pref this way ^^

Answer 7

The one you showed me?

Answer 8

Tan(45)=x/3 right?

Answer 9

Correct. the tan of 45 is 1 btw so its 1 = x/3

Answer 10

x=3

Answer 11

Or in other words 1*3.. So now that you got the length of 2 sides you can use Pythagorean theorem. To solve for the hypotenuse. (a^2 + b^2 = c^2)

Answer 12

Where do I plug them in?

Answer 13

Notice that this is a 45-45-90 triangle. You can use the Pythagoras theorem, with both legs = 3, and solve for the hypotenuse. Also, the ratio of the lengths of the sides of a 45-45-90 triangle is 1 : 1 : sqrt(2)

Answer 14

Let c be the Hypotenuse. So it would be (3^2 + 3^2 = c^2)
9+9=18
\[\sqrt{18}\] = 4.24
Or if you wanted to be more precise you could do simplify it to \[3\sqrt{2}\]

Answer 15

a^2+b^2=c^2
3^2+3^2=c^2

Answer 16

Thanks!

Answer 17

Correct.
9 + 9 = c^2
etc.

Answer 18

I think in your case tho 4.24 is plenty precise enough.

Answer 19

This is a trig problem

Answer 20

Why trig? Just good old Pythagoras is enough.

Answer 21

Yes it is, & @TwitchyJoe I do the same with this one right?

Answer 22

Both legs are "a"
a^2 + a^2 = 10^2

Answer 23

Yes only this time you use Sin.

Answer 24

So Sin(45) = x/10

Answer 25

\[-5\sqrt{2}\]

Answer 26

You are doing your math slightly wrong.. Its just Sin45 which is 0.7* 10

Answer 27

Opps i wrote 0.7, it should be 0.71*10

Answer 28

So your answer would be 7.1

Answer 29

Thank you again for explaining and being patient.

Answer 30

The answer would then be 71 right?

Answer 31

7.1 Yes. Also close the question after you are done.

Answer 32

Dont forget the ---> .

Answer 33

Trying to point to the dot lol

Answer 34

LOL okaaay, the length of the opposite side of 45 is 7.1.