Question

Two sides and an angle​ (SSA) of a triangle are given. Determine whether the given measurements produce one​ triangle, two​ triangles, or no triangle at all. Solve each triangle that results.  


a equals 9 comma


b equals 8 comma


A equals 50 degrees

Answer 1

Answer:

B = 42.9°

C = 87.1°

c = 7.4

Step-by-step explanation:

In this problem we are given two sides and one angle of a triangle ABC. The given values are:

a = 9

b = 8

A = 50°

In this case, there wil be only one solution, because the side opposite the given angle (side a) is longer than side b that was also given.

Calculating, let's the the law of sines.

$\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$

$\frac{sin 50}{9} = \frac{sin B}{8} = \frac{sin C}{c}$

Taking for A & B, we have:

$\frac{sin 50}{9} = \frac{sin B}{8}$

Let's cross multiply

(sin 50°)(8) = 9 sinB

Solving further,

$sin B = \frac{8 sin 50}{9}$

$sin B = \frac{6.128}{9}$

$B =sin^-^1(0.68)$

B = 42.9°

Since the total angle of a triangle is 180°, to find C, we have:

C = 180 - 50 - 42.9

C = 87.1°

To find the length of c, let's also use the sine formula.

$\frac{sin B}{b} = \frac{sin C}{c}$

$\frac{sin 42.9}{8} = \frac{87.1}{c}$

Cross multiplying

8c = 87.1 sin 42.9

$c = \frac{87.1 sin42.9}{8}$

c = 7.4