ABC, m<=56 degrees​, c=15 ​ft, and a=14 ft. Use the Law of Sines to find m<C.

Answer 1

You have to first identify which angle has measure of 56 degrees . Since we are given c=15ft,a=14ft. implies the angle measure we are talking about is the angle b which corresponds to the side b.

Using the law of sines

(sin(angle a))/ (side a) = (sin(angle c))/(side c) = (sin(angle b))/(side b)

Since this shape is a triangle implies that all the interior angles: angle a, angle b, and angle c add up to be 180 degrees. So (angle a)+ (angle c)= (180 -56) degrees= 124 degrees (since angle b is 56 degrees).

We have (sin(angle (124-c)))/(side a) = (sin(angle c))/(side c)= (sin(angle b))/(side b)

From the given info we have side a = 14 ft, side c = 15 ft, and angle b = 56 degrees.

Plug in the given terms in law of sines equations so that:

(sin(angle(124-c)))/(14) = (sin(56 degrees))/(side b) = (sin(angle c))/(15)

From all of this info you can figure it out!! To find the measure of angle c = answer!!

Answer 2

Hi Meggie,

Using the Law of Sines we can set up two equivalent fractions.

the sin C/c = sin A/a

plugging in we have sin C /15 = sin 56 degrees/14

sin (56) = .829

plugging in values the measure of angle C is 63 degrees