Question

Triangle ABC has the given measures. Solve the triangle(s), if any exist.

A = 162°, a = 6.1, b = 4

How many triangle(s) can possibly be formed?

Answer 1

1

12

6

2

Explanation:

on edge

Answer 2

Since A>90° and a>b, we can only form one triangle.
Lest solve it:
First we are going to use the law of sine to find the angle B:

`(SinB)/(b) = (SinA)/(a)`

`(SinB)/(4) = (Sin(162))/(6.1)`

`SinB= (4Sin(162))/(6.1)`

`B=arcSin((4Sin(162))/(6.1))`

`B=11.7`°

To find angle C, we are going to take advantage of the fact that the sum of the interior angels of a triangle is 180°:

`C=180-(162+11.7)`

`C=180-173.7`

`C=6.3`

To find the remaining side c, we are going to use the law of sines:

`(c)/(SinC) = (a)/(SinA)`

`(c)/(Sin(6.3)) = (6.1)/(Sin(162))`

`c= (6.1Sin(162))/(Sin(6.3))`

`c=3.6`

We can conclude that we can only form a triangle with the given measures.