Question

In each triangle below find the missing angles and sides. Show all of your work. In all questions m∠C=90°.

Answer 1

Find the following and show all work including the trigonometric ratios used:
The measure of angle A
The measure of angle B
The length of side AC

Answer 2

HELP

Answer 3

ill award a medal and fan

Answer 4

To find the measure of angle A you would analyze the triangle we know of the hypotenuse and the opposite side of the angle so we would use sine....

\(\Large{\sin (x)=\frac{ 4 }{ 10 }}\) Now we simplify to find x....

\(\LARGE\color{red}{x=\sin^{-1} (\frac{ 4 }{ 10 })}\) so what would angle A be?

Answer 5

@Prince1342 you there?

Answer 6

When inputting this equation in your calculator make sure it is set in degree mode instead of radian mode...

Answer 7

Yeah im trying to plug it in my calculator

Answer 8

Thanks for the tip! i forgot that

Answer 9

^^

Answer 10

I got 23.5781

Answer 11

Correct ^^

Answer 12

Really? Awesome!

Answer 13

What equation do i get to find the other angle?

Answer 14

Now we need to find angle B....Now we analyze the triangle once more we see that we know the hypotenuse and we see that the side 10 is next to the angle we want to know so it is now the adjacent angle....So since we know of the hypotenuse and the adjacent angle we would use cosine....

\(\Large\color{green}{\cos (x)=\frac{ 4 }{ 10 }}\) Now to simplify we get the variable x by itself....

\(\LARGE\color{red}{x=\cos^{-1} (\frac{ 4 }{ 10 })}\) What would angle B be?

Answer 15

Remember \(\LARGE{SOA}\), \(\LARGE{CAH}\), and \(\LARGE{TOA}\)

S=Sine
C=Cos
T=Toa

O=opposite side
A=adjacent side
H=hypotenuse

Answer 16

66.42

Answer 17

Correct once again ^^

Answer 18

Sweet!

Answer 19

Now to find AC we use Pythagorean Theorem we know of the hypotenuse and one leg so we input...

\(\LARGE{4^{2}+b^{2}=10^{2}}\) Simplify...

\(\LARGE\color{purple}{8+b^{2}=100}\) To get \(\large{b^{2}}\) by itself we subtract 100 by 8...

\(\LARGE\color{orange}{100-8=b^{2}}\) and we get \(\LARGE\color{green}{96=b^{2}}\)...

Now to get \(\large{b}\) by itself we would find the square root of \(\large{96}\)...

\(\LARGE\color{red}{b=\sqrt{96}}\)

Answer 20

9.79

Answer 21

Now you probably need to put this in radical form...

Answer 22

Yup ^^ that is the answer in decimal form, or do you need it in radical form?

Answer 23

It doesn't really specify actually

Answer 24

I guess I'll assume that decimal is ok

Answer 25

Well if it does need it in radical form....it is \(\LARGE{4\sqrt{6}}\)

Answer 26

Well we solved everything....hope I was helpful ^^

Answer 27

Should I put both?

Answer 28

You were EXTREMELY helpful, I feel a better understanding now thanks to you!!

Answer 29

Well if you compare on how you have been putting your answers before it would either be decimal or radical form but try decimal...^^ im glad I was....if you ever need help in the future just tag me in your question xD