Question

Find all the missing parts to the triangle below.

http://static.k12.com/eli/bb/817/-1/0/2_36847_44974/-1/5f949d8f893fa247cefb9c3be1a4130a44ba1245/media/d40ea57ffd4723c6bfdde50bf520f1b9aec65c92/mediaasset_651269_1.gif

Answer 1

@zepdrix @tkhunny @bibby

Answer 2

I guess one way to start would be...
we could find the length of side \(\Large\rm f\) using the Law of Cosines, yes?

Answer 3

I believe so.

Answer 4

\[\Large\rm f^2=15^2+28^2-2(15)(28)\cos(87^o)\]

Answer 5

That equals 31.06?

Answer 6

Ok great!
That's what I'm coming up with also.

I got 31.06505749, which I guess would round to 31.07.
No big deal though.

Answer 7

From there, Law of Sines would be a way to go.

Answer 8

How would I go about that?

Answer 9

\[\Large\rm \frac{\sin(A)}{a}=\frac{\sin(B)}{b}\]

Answer 10

This would allow us to solve for angle B in our problem.

Answer 11

\[\Large\rm \frac{\sin(78^o)}{31.07}=\frac{\sin(B)}{28}\]

Answer 12

We want to start by solving for sin(B).
So what should we do? :o

Answer 13

Sin 78=.98 so take that and multiply it by 28 and get 27.38

Answer 14

And divide by the 31, yes?

Answer 15

I suppose but that would give us .88 and I don't think that's right?

Answer 16

So that gets us to,\[\Large\rm \sin(B)=0.88\]

Answer 17

To solve for our angle B, we need to apply the inverse sine function to this.

Answer 18

If we rewrite this in terms of the inverse sine, our B and 0.88 will switch places.\[\Large\rm \sin^{-1}(0.88)=B\]

Answer 19

61.64!

Answer 20

Ok great!

To find the 3rd angle should be really nice and easy.
Recall that the interior angles of a triangle sum up to 180 degrees.

Answer 21

Yeah so the last angle would be 31.36, no?

Answer 22

Yes, good job ^^

Answer 23

Thank you.

Answer 24

np