Question

the two legs of a triangle are 300 and 150 m each, respectively. The angle opposite the 150 m side is 26 degree. What is the 3rd side?

Answer 1

Here's a graphic:

Answer 2

And here's the Law of Sines:

Answer 3

I got 341.78 m, am I right?

Answer 4

150/sin(26) = 300/ angle
Yes, this will just give you the second angle

Answer 5

snitch - I get 341.78 too

Answer 6

Thank you guys :D

Answer 7

Since this problem gives you side side angle, there can be another solution
197.49

Answer 8

can you teach me for the other alternative solution? :)

Answer 9

This is one of the cases of SSA where you'll get 2 possible triangles

See attached

Triangle ABC is one possible triangle.
Triangle ABD is another possible triangle.

Answer 10

Thank you @jim_thompson5910 :)

Answer 11

forgot to label BC. I used geogebra to make the triangles

Answer 12

Wow - I just made a graphic, but Jim's looks really good.

Answer 13

I had geogebra do all of the work @wolf1728
https://www.geogebra.org/

Answer 14

Can I download this for free?

Answer 15

yes you can also use it as a web app too, which means it runs without you having to download anything. I prefer the desktop version though

Answer 16

Thanks again guys :)

Answer 17

no problem

Answer 18

150/sin(26 degrees) = 300/ sin(Angle C)
sin(Angle C) = sin(26) * 2
sin(Angle C) = 0.43837 * 2
sin(Angle C) = 0.87674
Angle C = 118.748

Answer 19

Angle B = 35.252

Answer 20

Law of Cosines
b^2 = a^2+c^2 -2*a*c * cos(B)
b^2 = 150^2 + 300^2 -2*150*300 * cos(35.252)
b^2 = 112,500 -90,000 * 0.81662
b^2 = 112,500 -73,496
b^2 = 39004
b = 197.49

Answer 21

the answer should be 197.49?

Answer 22

thank you :D