How do you solve the triangle when given b = 15, c=8, a=15?

Question

3398 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-30T19:22:19

This is funny because there's a right triangle with sides a=15, b=8, and c=17. This is not that triangle ;-}

We have #a = 15#, #b = 15#, and #c = 8#.

Let's use the law of cosines to find angle C between the two 15's:

#c^2 = a^2 + b^2 - 2ab cos(C).#

Now put in what we know:

#8^2 = 15^2 + 15^2 - 2 * 15 * 15 * cos(C)#

#64 = 450 - 450 cos(C)#

#450 cos(C) = 450 - 64 = 386#

#cos(C) = 386/450 = 193/225.#

Now you can solve for C using a calculator:

#C = arccos(193/225) ~~ arccos(0.8578) ~~ 30.93^@#

The other two angles A and B are equal, and #A + B + C = 180^@#, so I leave that step to you!

...// dansmath strikes again! \\...