SOLVE USING LAWS OF COSINE! SUPER EASY!!! 10 POINTS!!! PLEASE HELP!!!!!?

Question

Use the cosine law to find the following: 

A) You have to find Angle A, and c, and side b! The measurements are that B is an angle of 48 degrees, small a is 6 cm, small c is 5 cm. 

B) In TUV: You have to find all the angles of TUV 

The measurements are small t is 5, small u is 4 and small v is 3 

Show your work!!!!!!

Answer 1

A) In ABC triangle B = 48°, a = 6cm and c = 5cm

To solve the triangle we need to find side b and angles A and C.

From the law of cosines b² = a² + c² - 2ac cosB

b² = 6²+ 5² - 2(6)(5) cos(48°)

b² = 36 + 25 - 60 (0.6691)

b² = 61 - 40.14

b² = 20.854

b = 4.566

b = 4.57

Now we use the law of sines to find other two angles.

SinA/a = sinB/b = sinC/c

sinA/a = sinB/b

sinA/6 = sin(48°)/4.57

sinA/6 = 0.7431/4.57

sinA/6 = 0.162

sinA = 0.972

A = sin^-1(0.972)

A = 76.40°

Now we find angle C ,which is easy using 'angles of triangle add to 180'.

C = 180° - (76.40°+ 48°)

C = 180 - 124.4

C = 55.6°

A = 76.40° ,C = 55.6°and b = 4.57 cm.

Answer 2

B) In TUV triangle t = 5, u = 4 and v = 3

u² = 16,  v² = 9 and  t² = 25.

Use the law of cosines first to find one of the angles.

cos A = (b² + c² - a²)/2bc

cosT = (u² + v² - t² )/2uv

cosT = (16 + 9 - 25)/24

cosT = 0

T = cos^-1 (0)

T = 90°

cosU = (v² + t² - u² )/2vt

cosU = (9 + 25 - 16 )/30

cosU = 18/30

cosU = 0.6

U = cos^-1 (0.6)

U = 53.13°

Finally, we can find angle V by using 'angles of a triangle add to 180°':

V = 180 - (90 + 53.13)

V = 180 - 143.13

V = 36.86°

The angles of TUV traingle are T = 90° , U = 53.13° and V = 36.86°.