Question

Tan C = 0.1405
B=0.5000

Answer 1

(28) B = 60°

(30) C = 8.00°

Explanation:

• Both problems require us to use inverse trigonometry to find the measures of angles B and C.

(28) Step 1:

• The cosine ratio is:

cos (reference angle) = adjacent/hypotenuse and we normally use it to find side lengths.

• Using the inverse cosine equation, cos^-1 (adjacent/hypotenuse) = angle, allows to find the measure (m) of B:

cos^-1 (0.5000) = m angle B

cos ^-1 (0.5000) = 60°

Thus the measure of B is 60°

(30) Step 1:

• the tangent ratio is:

tan (reference angle) = opposite/adjacent and we normally use it to find side lengths as well.

• Using the inverse tangent equation, tan^-1 (opposite/adjacent) = angle, allows us to find the measure of C:

tan^-1 (0.1405) = m angle C

tan^-1 (0.1405) = 7.997705648

tan^-1 (0.1405) = 8.00°

Thus, the measure of C is approximately 8.00°

• As long as you follow the steps I provided your teacher/instructor will hopefully accept C = 8.00° as an answer even though it's rounded
• You're also free to use the unrounded and more exact answer C = 7.997705648°