Question

How many possible triangles can be created if measure of angle B equals pi over 6 comma c = 10, and b = 5?1 triangle2 triangles0 trianglesCannot be determined based on the given information

Answer 1

1 triangle

Explanation:

Given information

The next step is to find the value of the third side by using the cosine rule

Let the third leg be a

`b^{^2\text{ }}=a^2+c^2\text{ - 2ac Cos B}`
`\begin{gathered} 5^2=a^2\text{ + }10^2\text{ - 2(5}*10)\text{ cos 30} \\ 25=a^2\text{ + 100 - 2(50) cos 30} \\ 25=a^2\text{ + 100 - 100cos 30} \\ \text{recall, cos 30}\degree\text{ = 0.8660} \\ 25=a^2\text{ + 100 - 86.6} \\ 25=a^2\text{ + 13.4} \\ \text{Subtract 13.4 from both sides} \\ 25-13.4=a^2+13.4-13.4 \\ 25-13.4=a^2 \\ 11.6=a^2 \\ a\text{ = }\sqrt[]{11.6} \\ a\text{ = 3.40} \end{gathered}`

Since we have been able to find the last leg and all the sides of the triangle are complete. Hence, we can say that we can create only 1 triangle

Recall, a triangle has 3 legs, and one angle. From the question given to us, we only have three sides and ONE angle. This can only create a triangle.