A= 32°, a = 19, b = 14

solve the triangle using the law of cos

The measures of the triangle are

Step-by-step explanation:

Step 1

Find the value of angle B

Applying the law of sines

we have

Substitute and solve for B

Step 2

Find the measure of angle C

we know that

The sum of the interior angles of triangle is equal to

so

we have

Substitute and solve for C

Step 3

Find the length of the side c

Applying the law of cosines

we have

substitute

The measures of the triangle are

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .