Question

How to find the angle measure of T?

Answer 1

I have no idea how to solve this since there's no other angle measure

Answer 2

Try the law of cosines. Do you know it?

Answer 3

Here is the Law of Cosines

Answer 4

@wolf1728 are you sure thats it? i thought it was a^2=b^2+c^2-2bc cosa ???

Answer 5

In your problem, let the three sides be t=7, r=11, s=10. Then the law of cosines becomes\[t ^{2}=r ^{2}+s ^{2}-2rs \cos \left( T \right)\]

Answer 6

ospreytriple's equation is better to use because itis written in terms of r, s and t

Answer 7

@ospreytriple would i just plug in the numbers from the triangle???

Answer 8

Rearranging, you get\[T=\cos ^{-1}\left(\frac{ r ^{2} +s ^{2}-t ^{2}}{ 2rs }\right)\]

Answer 9

@ospreytriple i'm really confused on how i would get a real answer out of that equation :(

Answer 10

just plug in the lengths of sides r, s, & t from the triangle.

Answer 11

@ospreytriple oh okay that's what i was wondering lmao

Answer 12

What do you get for an answer?

Answer 13

@ospreytriple 45.57

Answer 14

Not what I get. You want to try it again?

Answer 15

@ospreytriple i got 63.25 :(

Answer 16

@ospreytriple i got 63.25 :(

Answer 17

@ospreytriple T=10? r=7? s=11?

Answer 18

No. t=10. You are trying to find angle T.

Answer 19

briana
r^2 = 121 s^2 = 100 t^2 = 49

r^2 + s^2 -t^2 = 172
agreed?

Answer 20

I think having 2 people explain things to a third gets a bit confusing
good luck briana and osprey :-)

Answer 21

@ospreytriple i listed those numbers because those are the ones you substitute in, right??

Answer 22

Ok. Evaluate the above equation for T by using the values of r, s, & t from the triangle.

Answer 23

@ospreytriple i know but i'm just asking if those are the numbers i use ??? like those are the correct ones for the substitution

Answer 24

I believe those are the side lengths from the triangle, yes.

Answer 25

\[T=\cos ^{-1}\left( \frac{ 11^{2}+10^{2} -7^{2}}{ 2\left( 11 \right)\left( 10 \right) } \right)\]

Answer 26

@ospreytriple yeah i jsut did that and my answer came out to be 63.25 again

Answer 27

What do you get for the value of the numerator?

Answer 28

@ospreytriple 70

Answer 29

Not quite.\[11^{2}+10^{2}-7^{1}=121+100-49= ?\]

Answer 30

Should be 7^2. Sorry.

Answer 31

@ospreytriple oh oops 172

Answer 32

Great. Now the denominator is\[2\left( 11 \right)\left( 10 \right)=?\]

Answer 33

@ospreytriple 220

Answer 34

Terrific so\[T=\cos ^{-1}\left( \frac{ 172 }{ 220 } \right)=?\]

Answer 35

@ospreytriple the calculator i'm using says 63.25???

Answer 36

@ospreytriple wait nevermind 38.64

Answer 37

Now you got it. Good job.

Answer 38

@ospreytriple sorry fro taking so long :( this unit is really messing me up

Answer 39

You're welcome. Those pesky calculators :)