Question

Solve for the missing length and the other two angles in the triangle below.

I will add an attachment! Thank you!

Answer 1

@zepdrix

Answer 2

@mathmate could you help please?

Answer 3

Typically, when two sides of a triangle and the included angle is known, you can use the cosine rule to find the third side, and then sine rule to find the remaining angles.

Answer 4

Okay the cosine rule is a^2=b^2+c^2-2bc cosA
So if I plug that in i get a^2=4^2+3^2-2(4)(3) cos(15 degrees)
a^2 is approximately 1.8
sqrt 1.8 = aproximately 1.35
Is that right??

Answer 5

Yes, 1.348251 to be closer, but yes, 1.35 is correct!

Answer 6

Thank you! I have another question that is similar to this but the cosine rule does not work. I am supposed to find length a.

Answer 7

However, you need more figures to do the sine rule calculations, or else you angles will be off!

Answer 8

For my first question. To find the angles would I set up ratios?
If so, i got 1.8/ sin(15)= 4/ sin b
Then i would cross multiply??

Answer 9

Exactly, but 1.348/sin(15)...

Answer 10

oh yeah. how about my second problem?

Answer 11

The same strategy for the second problem, since two sides and included angle are known.
The fact that 108 > 90 degrees does not matter, because cos108 will then be negative, and everything will work out.

Answer 12

So use the cosine rule?

Answer 13

Yep, cosine rule, followed by sine rule (whenever 2 sides and included angle are known).

Answer 14

I get:
a^2=13^2+11^2-2(13)(11) cos(106)
but when i plug this in i get- 368.32 and the square root it and get: 19.205 is that right?

Answer 15

I get 19.4520 , you can double check my number.
Sorry, gtg.

Answer 16

I still get 19.205 but thank you!

Answer 17

I think the angle is 108, unless I made a mistake. @haileycaroen

Answer 18

I think the angle is 108, unless I made a mistake. @HaileyJCaroen