We know that the side opposite the biggest angle is the longest; while side opposite shortest angle is the smallest. So, side with length 9 is opposite the angle of 50°. So, longest side would be opposite angle of 70°.
To solve this, simplest would be the use of the law of sines here:
If sides of a triangle are a,b,c - opposite the angles A, B, C respectively, then
a/sin(A) = b/sin(B) = c/sin(C)
In this case, use only a, b and A, B
where;
a=longest side length (unknown)
A = 70°
b = shortest side length = 9
B = 50°
Now, we can easily solve for 'a' as:
a = (b * sin(70°))/(sin(50°))
Use the scientific calculator in the PC to find out the values of sin(70°) and sin(50°)
here's what I got:
sin 70° = 0.9396
sin 50° = 0.7660
Substituting these values in the formula above, we get
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Verified answer
Solve it using a/sin(A)=b/sin(B)=c/sin(C)
We know that the side opposite the biggest angle is the longest; while side opposite shortest angle is the smallest. So, side with length 9 is opposite the angle of 50°. So, longest side would be opposite angle of 70°.
To solve this, simplest would be the use of the law of sines here:
If sides of a triangle are a,b,c - opposite the angles A, B, C respectively, then
a/sin(A) = b/sin(B) = c/sin(C)
In this case, use only a, b and A, B
where;
a=longest side length (unknown)
A = 70°
b = shortest side length = 9
B = 50°
Now, we can easily solve for 'a' as:
a = (b * sin(70°))/(sin(50°))
Use the scientific calculator in the PC to find out the values of sin(70°) and sin(50°)
here's what I got:
sin 70° = 0.9396
sin 50° = 0.7660
Substituting these values in the formula above, we get
a = (9 * 0.9396)/0.766
= 11.03
So you now have your answer: longest side is 11
12.5