Question

Find the measure of angle P in the triangle below.

Answer 1

Do you know the Law of Cosine?

Answer 2

sorta @science0229

Answer 3

What is it?

Answer 4

Law of Cosines is c^2= a^2 + b^2 - Ab cos ( c )

Answer 5

@science0229

Answer 6

close.
It's\[c^2=a^2+b^2-2ab \cos \theta\] where theta is the angle between a and b

Answer 7

theres not angle given

Answer 8

No. But all three sides are given, right?

Answer 9

Your goal is to find that angle.

Answer 10

explain how to get it

Answer 11

Since you have to find angle P, the 2 sides that has P between are RP and QP, right?

Answer 12

yea

Answer 13

so, a=RP=60 and b=QP=36
Automatically, c=RQ=48

Answer 14

i understand that 60 is an angle right

Answer 15

No. All of the numerical values right now are the sides of the triangle.

Answer 16

ok

Answer 17

Do understand so far?

Answer 18

oh yea i do i get it

Answer 19

You should get up to here:\[48^2=60^2+36^2-2(60)(36)\cos \theta\]

Answer 20

ok

Answer 21

so u plug it in ?

Answer 22

Solve for cos theta to get \[\cos \theta=\frac{ 60^2+36^2-48^2 }{ 2(60)(36) }=\frac{ 3 }{ 5 }\]

Answer 23

ok let me try doing this on my calculator real quick

Answer 24

what do i do with 3/5

Answer 25

have you learned inverse trig function, yet?
Something like \[\cos^{-1} \] or arccos

Answer 26

not that i remember

Answer 27

Ok. It'll be brief

Answer 28

ok

Answer 29

thx for explaining this :)

Answer 30

Inverse Trig Function is literally the inverse of trig function.
In other words, it "reverses" the trig function.

Answer 31

Mathematically, it would be this:\[y=\sin(x)\]
To "reverse" this...\[x=\sin(y)\]
Solve for y. This is when the inverse trig function come into play.
Mathematicians defined the inverse trig function as this:\[y=\sin^{-1} (x)\]

Answer 32

so then what

Answer 33

For our original problem, we came to the conclusion that \[\cos \theta=\frac{ 3 }{ 5 }\]

Answer 34

This means that for some kind of value theta, cos(theta) is 3/5.
To find this theta, we use the definition of inverse trig function:\[\theta=\cos^{-1} \frac{ 3 }{ 5 }\]

Answer 35

Are you lost?

Answer 36

kinda

Answer 37

Yeah. I'm not a very good explainer...
What grade are you?

Answer 38

sophmore

Answer 39

Then I'm thinking that you'll learn this soon in your math class.

Answer 40

whats the answer at least

Answer 41

do you have a calculator?

Answer 42

yea

Answer 43

what kind?

Answer 44

Ti-84 plus

Answer 45

Do you have to find this angle in degrees or radians?

Answer 46

radians i think

Answer 47

Then put your calculator in radian mode.
You know how to do it, right?

Answer 48

um I'm trying right now

Answer 49

http://www.youtube.com/watch?v=9Dg56o6G0MI

Answer 50

thx

Answer 51

ok its in radians

Answer 52

@science0229

Answer 53

Because 3/5=0.6, type in 0.6

Answer 54

Now, press the 2nd button and the sin button

Answer 55

sin of 0.6?

Answer 56

Wait.
Do 2nd button and the COS button
my mistake

Answer 57

You must press 2nd first

Answer 58

what did you get?

Answer 59

.92

Answer 60

That's your answer, then.

Answer 61

.92 radians

Answer 62

thx for being patient with me and teaching me

Answer 63

Welcome :)

Answer 64

byeeee