# Math: law of cosines, hw help?

### 3 Answers

- Engr. RonaldLv 75 months agoFavorite Answer
Apply the law of cosine

∠B = 180 - 111 = 69°

solving for side b

b = √[a^2 + c^2 - 2accos(B)]

b = √[19^2 + 10^2 - 2(19)(10)cos(69)]

b = 18.022 or 18

apply law of sine to solve Angle C

.....b..............c

--------- =-----------

..sin(B)....sin(C)

...18.............10

----------- =---------

..sin(69)...sin(C)

18sin(C) = 10sin(69)

................10sin(69)

sin(C) = ----------------- <-----------closest answer on choice D

.......................18

...................................10sin(69)

Answer is D. sin(C) =---------------

.......................................19

- KrishnamurthyLv 75 months ago
In △ABC, a = 19, c = 10, and m∠A = 111°.

Which statement can be used to find the value of C?

The Law of Cosines (also called the Cosine Rule) says:

a^2 = b^2 + c^2 − 2bc cos (A)

19^2 = b^2 + 10^2 - 20b cos (111°)

b(b - 20 cos (111°) = 29*9

b (b + 20 sin((7 π)/60)) = 261

- fcas80Lv 75 months ago
Law of Sines: sinC/10 = sin111/19

sinC=10 * sin111 / 19. But sin111 = sin69

sinC = 10 * sin69 / 19

answer D