Triangle ABC has angles of 51 degrees, 54 degrees and 75 degrees with lengths of 17 and 16 Triangle DEF has angles 51 degrees, 54 degrees and 75 degrees with one length of 45 and x solve x
In a triangle, the sum of all angles is always 180 degrees. Therefore, the remaining angle of triangle ABC can be found by subtracting the given angles from 180:
180 - 51 - 54 - 75 = 180 - 180 = 0 degrees
This means that triangle ABC is not possible as the remaining angle is 0 degrees.
However, in triangle DEF, we know two angles (51 and 54 degrees) and one side length (45). We can use the Law of Sines to find the missing side length x.
Let's use the Law of Sines formula:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the side lengths opposite to angles A, B, and C respectively.
We have angle A = 51 degrees, angle B = 54 degrees, side a = 45, and side b = x.
Plugging in the values:
45/sin(51) = x/sin(54)
Now, we can solve for x:
x = (45 * sin(54)) / sin(51)
x ≈ (45 * 0.809) / 0.788
x ≈ 46.305
Therefore, the missing side length x in triangle DEF is approximately 46.305.