Question

PLEASE HELPPPP!!!!

Solve triangle ABC if m b=
C=
Solve triangle ABC if m I
C=
How do you know that this problem is not the ambiguous case?

Answer 1

Using the law of sines, the triangles are solved as: 2. m∠A = 87°; b ≈ 4.98; c ≈ 1.95 3. B = 21°; m∠C = 124°; c ≈ 16.

How to apply the Law of Sines?

To solve triangle ABC, you can use the fact that the sum of the angles in a triangle is always 180 degrees.

2. Given:

m∠B = 71°,

m∠C = 22°, and

side a = 5.20.

Find m∠A:

m∠A = 180° - m∠B - m∠C

m∠A = 180 - 71 - 22

m∠A = 87°

Use the Law of Sines to find the other two sides (\(b\) and \(c\)) in the triangle:

`(a)/(\sin A) = (b)/(\sin B) = (c)/(\sin C)`

`b = (a \cdot \sin B)/(\sin A) = (5.20 \cdot \sin(71^\circ))/(\sin(87^\circ))`

b ≈ 4.98

`c = (a \cdot \sin C)/(\sin A) = (5.20 \cdot \sin(22^\circ))/(\sin(87^\circ))`

c ≈ 1.95

3. Given:

m∠A = 35°, a = 11; b = 7

Find m∠B using a/sin A = b/sin B:

11/sin 35 = 7/sin B

sin B = 7 * sin 35 / 11

sin B = 0.3650

`B = sin^(-1)(0.3650)`

B = 21°

m∠C = 180 - 35 - 21

m∠C = 124°

Find c using a/sin A = c/sin C:

11/sin 35 = c/sin 124

c = 11 * sin 124 / sin 35

c ≈ 16