Use the Law of Cosines, a2=b2+c2−2bc⋅cosA, to find the value of angle A in a right triangle, where a=7, b=24, and c=25
To find angle A in the right triangle, we will use the Law of Cosines formula:
a^2 = b^2 + c^2 - 2bc*cosA
Substitute the given values:
7^2 = 24^2 + 25^2 - 2*24*25*cosA
49 = 576 + 625 - 1200*cosA
49 = 1201 - 1200*cosA
-1152 = -1200*cosA
cosA = -1152 / -1200
cosA = 0.96
To find angle A, take the inverse cosine of 0.96:
A = cos^(-1)(0.96)
A ≈ 16.26 degrees
Therefore, angle A in the right triangle is approximately 16.26 degrees.