Question

can someone please help me ive been stuck on this for a month and im so behind :(

Answer 1

Are you ready?

Answer 2

yes

Answer 3

For number 4, we would need to find AC first, because we can use it to find the angles we need.

Answer 4

Are you familiar with the Pythagorean theorem?

Answer 5

not really... all ive been seeing is a^2+b^2=C^2

Answer 6

Here, For any right triangle, the sum of the square of the opposite and adjacent sides equals the square of the hypotenuse.

Answer 7

ok so for my problem how do i plug it in ? 10+4=c?

Answer 8

In your problem, we have

Answer 9

Can you see that AC corresponds to "a" in the example I showed?

Answer 10

what do you mean when you put corresponds

Answer 11

In my example "a" is the lower side of the triangle, in your problem, AC is also the lower part of the triangle. Same sides.

Answer 12

oh ok

Answer 13

i see that

Answer 14

Good. Since its that way we can solve for AC. Since \[c^{2} = a^{2} + b^{2} \]
We can solve for a to give us \[a = \sqrt{c^{2} - b^{2}}\]
That also means we can solve for AC to give us
\[AC^{2} = \sqrt{10^{2} - 4^{2}}\]

Answer 15

oh ok so then do i solve the last equation?

Answer 16

Yes. Sorry I made a mistake, it should be AC NOT AC^2

Answer 17

ok so how do i do that minus 10^2-4^2 and that gives me 84

Answer 18

\[\sqrt{84}\]

Answer 19

and do i solve that?

Answer 20

Yes.

Answer 21

\[2\sqrt{21}\]

Answer 22

or 9.1651513

Answer 23

Smart!

Answer 24

thank you :) so do i do that for all of them and can you help me with another one

Answer 25

Now we have figured out AC. Time to get angles!

Answer 26

oh yeah lol almost forgot i wasnt done

Answer 27

So do you know trig ratios?

Answer 28

no :/

Answer 29

so 10= 4/c

Answer 30

Oh I forgot something,

Answer 31

oh idk how to do that

Answer 32

Okay, a little teaching on trig ratios. In a right triangle we have the following properties,

Answer 33

so sin(a)= 4/10

Answer 34

Excellent!

Answer 35

what do we do after that

Answer 36

To find A itself we need to introduce something else, its called the inverse sine. It works this way \[\sin \theta =\frac{ a }{ c }\]
\[\theta = \sin^{-1} \frac{ a }{ c }\]

Answer 37

I did this \[\sin^{-1} (\sin \theta) = \sin^{-1} \frac{ a }{ c }\] Which then gave me \[\theta = \sin^{-1} \frac{ a }{ c }\]

Answer 38

do i plus a in or do we just leave it like that

Answer 39

Because of your question you should plug in a and c.

Answer 40

ok so it would be \[\Theta= \sin -1 4/10 \]

Answer 41

opps o forgot to space

Answer 42

but is that negative 1 a exponent or a actual -1

Answer 43

Its just a symbol. It means nothing.

Answer 44

oh ok

Answer 45

So it should be \[\sin^{-1} \frac{ 4 }{ 10 } = \sin^{-1} \frac{ 2 }{ 5 }\]

Answer 46

how do i solve that

Answer 47

Use your calculator. Press shift + sin first, then 2/5, then =

Answer 48

i got .4

Answer 49

Nope. Try again. It should be 23.5 degrees.

Answer 50

ohhh i got it

Answer 51

and thats for A

Answer 52

To find B. We do the same thing. The side opposite B is 9.1 (Remember this is AC we solved for), and the hypotenuse is c = 10. So solve for B using what I showed.

Answer 53

is b 66.42 degrees

Answer 54

Yes.

Answer 55

yayyyyy :)

Answer 56

You learn quick.

Answer 57

only because you actually helped me :)

Answer 58

:)

Answer 59

Can you solve number 5 using all you've learned so far?

Answer 60

yes i think i can finish the rest by myself thanks for the help! you made my day :)))))

Answer 61

Good stuff!