Question

@potatoeewedge

1. If m∠B = 32°, and AB = 12 cm, what is AC?

[See Attachment]

(Enter your numeric answer. Round to the nearest hundredth.)



2. If m∠B = 41°, and AB = 5 cm, what is BC?

[Same Attachment]

(Enter your numeric answer. Round to the nearest hundredth.)



3. If m∠A = 56°, and BC = 24 cm, what is AC?

[Same Attachment]

(Enter your numeric answer. Round to the nearest hundredth.)

Answer 1

The given problem is a right triangle, we can use Pythagorean theorem and SOH CAH TOA in solving the unknown.
For item#1,
sin B = AC/AB
sin 32° = AC/12
AC=6.36 cm

For item#2,
cos B = BC/AB
cos 41° = BC/5
BC = 3.77 cm

For item#3,
tanA=BC/AC
tan 56 = 24/AC
AC = 16.19 cm