35.7°
To find the smallest angle in a triangle, we can use the Law of Cosines. The formula for the Law of Cosines is:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we know that side XY is 3.5 and side YZ is 8. We want to find the angle at vertex Z (opposite side YZ).
Plugging the values into the Law of Cosines formula:
8^2 = 3.5^2 + XZ^2 - 2(3.5)(8) * cos(Z)
64 = 12.25 + XZ^2 - 56 * cos(Z)
Rearranging the equation:
XZ^2 = 64 - 12.25 - 56 * cos(Z)
XZ^2 = 51.75 - 56 * cos(Z)
We don't know the exact lengths, but we know that the smallest angle is opposite the smallest side. Since we are looking for the smallest angle, we assume that side XZ is the smallest side, therefore cos(Z) should be the largest. cos(90°) = 0 is the largest value of cos(Z), so the smallest angle would be 35.7° (rounded to the nearest tenth).
For △XYZ, what is the measure of the smallest angle to the nearest tenth of a degree?
A picture of an inverted right triangle XYZ is shown. Side XY has a length of 3.5 and Side YZ has a length of 8. Side XZ is unlabeled.
11.5°
23.6°
90°
35.7°
1 answer