Question

(1 point 16 18 I W AB has length 18 and AC has length 16, find: • The length of MC . The measure of angle B in degrees): . The measure of angle in degrees): If you use a calculator to find a decimal approximation, your answer must be accurate to at least 3 decimal places If you're using a calculator, be sure that your calculator is set to degrees, not radians You are also allowed to use the inverse trig functions in your answer instead of using a calculator. (sin(x) can be entered as arcsine), asins, er sinn-1) Note: You can earn partial credit on this problem Preview My Answers Submit Answers MacBook Air SO DD CA DU F $ ) # 3 % 5 & 7 6 8 0 E R T Y U 0 Р D F G H J K L

Answer 1

1) Length of BC :

BC² = AC² + AB²

BC² = (16)² + (18)²

BC² = 256 + 324 = 580

BC = sqrt(580) = 24.083

Hence, length of BC = 24.083

Now, angle B:

tan $\theta$ = 16 / 18 = 8 / 9

$\theta$ = tan^-1(8/9) = 41.633 degrees

Measure of angle B is 41.633. degrees

Now, measure of angle C = 90 - 41.633 = 48.367.degrees

2) Length of AC:

BC² = AC² + AB²

(15)² = AC² + (9)²

225 - 81 = AC²

AC = sqrt(144)

AC = 12

Now, measure of angle B:

tan $\theta$ = 12 / 9 = 3 / 4

tan $\theta$ = 0.75

$\theta$ = tan^-1(0.75) = 36.869 degree

Measure of angle B is 36.869 degrees.

Now, measure of angle C is ( 90 - 36.869 ) = 53.131 degrees

3) Length of AC:

BC² = AC² + AB²

(19.1)² = AC² + (3.7)²

364.81 - 13.69 = AC²

AC² = 351.12

AC = sqrt (351.12) = 18.738

Now, the measure of angle B:

tan $\theta$ = 18.738 / 3.7 = 5.064

$\theta$ = tan^-1(5.064) = 78.830 degrees.

So, measure of angle B is 78.830 degrees.

Also, the measure of angle C is (90 - 78.830) =11.171 degrees.

4) Length of AB:

BC² = AC² + AB²

(11)² = (5)² + AB²

121 - 25 = AB²

AB = sqrt(96) = 9.797

Now, measure of angle B :

tan $\theta$ = 5 / 9.757 = 0.5124

$\theta$ = tan^-1 ( 5 / 9.757 )

$\theta$ = 27.130 degrees.

Now, the other angle 90 - 27.130 = 62.face rhaping