How many triangles exist when the measure of angle B is 100 degrees, a =10 and b=5?
a. none
b. 1 triangle
c. 2 triangles
I have already solved this and I have found that there will be no triangle because by using the law of sines I found that the value is bigger than 1.
So, I am unsure if my answer is correct?
correct,
I attempted to find angle A
sinA/10 = sin100°/5
sinA = 10sin100/5 = appr 1.97
not possible , so no such triangle can exist
Trust you math ability
To determine the number of triangles that can be formed with the given information, you are correct in using the Law of Sines. The Law of Sines states that, in a triangle, the ratio of the length of a side to the sine of the opposite angle is constant.
In this case, you have angle B with a measure of 100 degrees, side a with a length of 10, and side b with a length of 5. To apply the Law of Sines, you'll need to find the sin(100°).
Using a scientific calculator, you can easily find the sine of an angle. By calculating sin(100°) and dividing side a (10) by sin(100°), you'll get the value of a/sin(100°).
If the value of a/sin(100°) is greater than or equal to 1, it means that a triangle cannot be formed with the given lengths of sides. However, if the value is less than 1, it means that there can be one or two possible triangles.
In this case, you have correctly determined that the value of a/sin(100°) is greater than 1, indicating that no triangle can be formed. Therefore, your answer of "none" is correct (option a). Well done!