Does this result in no triangle, 1 or 2 triangles? If so, then solve.
B= 88 degrees, b= 4 and a=23.
I know that A= (sin 88)(23)/(4)= A=5.74 degrees
C= 180-5.74-88= C=86.26 degrees
c=(sin86.26)(4)/(sin 88)= c=3.99
My question is how do you know if it's 0,1, or 2 triangles. And if so, what do you do next?
Remember, it's
sinA/a = sinB/b
What you have is sinA = 5.74, not A=5.74
There is no angle with sine of 5.74.
Clearly there will be no triangle here. Sin 88 is almost 1, so 23/4 that will be much more than 1.
Thank you Steve.
To determine if there are 0, 1, or 2 triangles in a given scenario, you can use the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In your case, the lengths of the sides are given as a=23, b=4, and c=3.99. To find out if a triangle can be formed, you need to check if the sum of two sides is greater than the third side for all possible combinations.
Let's consider the combinations:
1) a + b > c: 23 + 4 > 3.99
2) a + c > b: 23 + 3.99 > 4
3) b + c > a: 4 + 3.99 > 23
From the calculations, it is evident that all three combinations satisfy the Triangle Inequality Theorem. Therefore, a triangle can be formed with the given side lengths.
Now that you know a triangle can be formed, you can proceed to solve for the remaining angles and sides using the given information.