Solve for the missing length and the other two angles in the triangle below.

Part 1 - use law of cosines to find the missing 3rd side

Part 2- use either the law of cosines or the law of sines to find the measure of angle C

Part 3- Use any method you like to find the measure of angle B

The triangle is missing, so i have attached it.

1) 3rd side = 12.92

2)angle C = 82°

3)angle B = 44°

Step-by-step explanation:

1) To find the missing 3rd side which is opposite to angle A, using cosine rule, we have

a² = b² + c² - 2bc•cosA

From the image,

b = 7.4 and c = 15.8 while A = 54°

Thus,plugging in relevant values ;

a² = 7.4² + 15.8² - 2(7.4*15.8)•cos54

a² = 54.76 + 249.64 - 137.45

a² = 166.95

a = √166.95

a ≈ 12.92

2) Using sine rule, we can find angle C.

Thus,

a/sinA = c/sinC

So, sin C = (c*sinA)/a

c = 15.8

a = 12.92

A = 54°

Plugging in the relevant values;

sin C = (15.8*sin54)/12.92

sin C = 0.98936

C = sin^(-1)0.98936

C ≈ 82°

3) to get angle B, we know that sum of angles in a triangle = 180.

Thus,

A + B + C = 180

So,54 + B + 82 = 180

B + 136 = 180

B = 180 - 136

B = 44°

its d. the first coordintaes are 10,32

step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12