Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.

Question

There may be two triangles, one triangle, or no triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Enter all angles in degrees. Round your answers to one decimal place. Below, enter your answers so that ∠A₁ is smaller than ∠A₂.)

b = 49,   c = 46,   ∠C = 32°

∠A₁

    ∠A₂

 °∠B₁

°∠B₂

°a₁

a₂

Answer 1

b=49, c=46 C=32

what are the other sides and angles?? and how many triangles? 0, 1 or 2? 2 about

A=2 B=146, a=4

or

A=114, B=34, a= 80

both obtuse scalene triangles

use a triangle solver online, easiest way to do the problem

check your answers to see if they make sense

no side can be longer than sum of the other 2 sides

no side can be shorter than the difference of the other 2 sides

sum of 3 angles = 180

longest angle is opposite longest side

shortest angle is opposite shortest side

they check out

Answer 2

sin32°/46 = sinB / 49

sinB = 49sin32° / 46 = 0.5546792

∠B = Sin^-1(0.5546702) or 180º - Sin^-1(0.5546792) = 34.4° or 145.6°

First triangle: ∠C = 32°, ∠B = 34.4°, ∠A = 113.6°, b = 49, c = 46, use Law of Sines to find a

Second triangle: ∠C = 32°, ∠B = 145.6°, ∠A = 2.4°, b = 49, c = 46, use Law of Sines to find a

Answer 3

If 46 = hypotenuse, one triangle

If 46 < hypotenuse, one triangle

If 46 > hypotenuse, two triangles.

Draw and label a diagram and answer.