How many triangles exist that fit the following criteria?B=80°𝐵=80°, a=8𝑎=8, b=5
Question
How many triangles exist that fit the following criteria?B=80°𝐵=80°, a=8𝑎=8, b=5
Solution
The given triangle is an oblique triangle with one angle (B) and two sides (a and b). We can use the Law of Sines to solve this problem.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.
So, we have:
a/sinA = b/sinB
Substituting the given values:
8/sinA = 5/sin80°
Solving for sinA:
sinA = 8*sin80°/5
Calculating the value:
sinA = 1.52 (which is not possible because the value of sine cannot be greater than 1)
Therefore, no triangle can exist with the given measurements.
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