Question

Could I find two missing angle measures if I know some of the side lengths of a right triangle?

Answer 1

AB = 8
BC = 6
CA = 10
Angle B = 90 degrees

Answer 2

Can someone help show the steps to find the missing angles? like step by step?

Answer 3

@Preetha @chmvijay @abb0t

Answer 4

@goformit100 @satellite73 @skullpatrol @.Sam. @amistre64 @uri @kelliegirl33 @SWAG
can u help him out

Answer 5

Thanks @chmvijay :)

Answer 6

@thomaster Do you have any idea? :/

Answer 7

Sure use trig

Answer 8

Are you familiar with SOH CAH TOA?

Answer 9

a tad, but i never fully understood it

Answer 10

Ok look SOH CAH TOA is a memory trick to remember the following...

Answer 11

\[ \sin A = \frac{ opposite leg }{ hypotenuse }\] \[ \cos A = \frac{ adjacent leg }{ hypotenuse }\] \[ \tan A = \frac{ opposite leg }{ adjacent leg }\]

Answer 12

A is the angle. Opposite leg means the leg across from the angle. Adjacent leg means the leg that is "hooked into" or touchig the angle (the leg not the hypotenuse) and hypotentuse the longest side (the one across from the right angle)/.

Answer 13

SO if you pick an angle that you want to find. Which one do you want to start with?

Answer 14

lets try angle a

Answer 15

@Paynesdad

Answer 16

Ok so now since you are looking for the angle you need to know at least two sides do in fact you know all three so let's pick any two of the three so which ones do you want to pick?

Answer 17

ab and bc?

Answer 18

@Paynesdad

Answer 19

So compared to A is AB the opp side, adj side or the hyp?

Answer 20

adj side right?

Answer 21

right and what about BC?

Answer 22

compared to a? opp side?

Answer 23

@Paynesdad

Answer 24

Sorry...Had to take care of something...yep BC is opp of A so you have the adjacent side and the opp side which trig function doies that indicate that you should use?

Answer 25

tan a im guessing

Answer 26

@Paynesdad

Answer 27

@Luigi0210 do you have any idea whats next?

Answer 28

Right

Answer 29

so you write....Tan of the angle equals the opp leg value over the adjacent leg value...or Tan A = 6/8

Answer 30

would that change to 3/4?

Answer 31

Well yes but I would just write it as a decimal because you will use you calculator soon anyway.

Answer 32

so Tan A = 0.75

Answer 33

Now you have to remove the Tan from the A or as I like to say UNDO the tangent. SO in algebra if you have 6x = 12 and you want to get rid of the 6 times x so it is just x ... you divide both sides by 6 to undo the 6 times ... right?

Answer 34

yes, so divide both sides by tan?

Answer 35

no because tan isn't a number it is a function Tan A doesn't mean Tan times A ... it is a special function of its own... Tan A means the Tangent of A. so to undo Tan A, I have to have a reverse function of Tan just like the reverse function of times is divide and vice versa

Answer 36

so the reverse function or the undo function of"Tangent of" is"Inverse Tangent of" or in symbols the inverse of Tan is \[tan^-1\]

Answer 37

So you want to undo Tan in the equation Tan A = 0.75 so ...

you take the Tan^-1 of both sides like this...
\[tan^-1 (tan A) = tan^-1 (0.75) \]

Answer 38

Now on the left hand side the tan-1 and the tan cancel just like in 6x/6 the 6 times and the 6 divide cancel to leave just x. so the left hand side of the equation above goes from

\[tan^-1 (tan A) =\] to just
A =

Answer 39

and on the right hand side you have \[tan^-1 (0.75)\] which you just put in your calculator to get a value ... make sure your calculator is in degrees mode. The value you get in your calculator should be the size of A in degrees.

so you final answer is A = (whatever number is in your calculator) it should be bigger than 30degrees but smaller than 45.

Answer 40

Alright, well i know what to do, but i just dont have a scientific calculator, i have a plain one:(

Answer 41

@Paynesdad

Answer 42

Do you have a calc on your computer?

Answer 43

yes but its a simple one, only basic functions and the "M+" and "MC", and "M-"

Answer 44

Usually in the view menu of that calculator is a choice to change it over to a scientific calc. you could try that.

Answer 45

oh sweet okay it worked, so what would i plug in exactly?

Answer 46

Make sure the calc is set for degrees.

Answer 47

so you should have shown the following work...

Answer 48

deg means degrees right? thats what it says

Answer 49

\[tan A = \frac{6}{8} = 0.75\] \[tan^-1 (tan A) = tan^-1(0.75)\] \[A = ______\]

Answer 50

yes deg means geree mode...Now type in your calc 0.75

Answer 51

then the "Inv" (Inverse) button.

Answer 52

then "Tan"

Answer 53

you could then hit equal...
What do you get?

Answer 54

none of the calculators have inv on it:/

Answer 55

well i used this one " https://www.google.com/search?q=scientific+calculator&oq=scien&aqs=chrome.2.0j69i57j0l2j69i62l2.2413j0&sourceid=chrome&ie=UTF-8#bav=on.2,or.r_cp.r_qf.&fp=81bbfe24b99ff94c&q=scientific%20calculator&safe=off " and it said error

Answer 56

@Paynesdad

Answer 57

@Luigi0210 im on the last part of this, and he left. you know the rest?

Answer 58

@dan815 hi luigi said to get you to help with the end of this problem?:)

Answer 59

is it the problem at the start of this conversation?

Answer 60

Sorry I am back... not sure why the calculator does not work. Use the google calc that you have but type inv then tan then 0.75... try that

Answer 61

okay i got 0.64, would that be correct?

Answer 62

That's in rad click the rad button at the top and do it again in degrees.

Answer 63

36.86?

Answer 64

There you go...Now that you have two angles and you know all three add to 1800 you should be able to find the third.

Answer 65

54?

Answer 66

yep! good job... Glad we could finally get this done.

Answer 67

thank you so much you dont understand how much that helped me!