Use the stated variant of the Law of Cosines, a2=b2+c2−2bc⋅cosA , to find the value of angle A in a right triangle, where a=5 , b=12 , and c=13 . Round your answer to the nearest whole number.
We are given a right triangle with sides a=5, b=12, and c=13.
To find angle A, we can use the variant of the Law of Cosines which states:
a^2 = b^2 + c^2 - 2bc * cosA
Plugging in the given values, we have:
5^2 = 12^2 + 13^2 - 2(12)(13) * cosA
Simplifying, we have:
25 = 144 + 169 - 312 * cosA
Combining like terms:
25 = 313 - 312 * cosA
Subtracting 313 from both sides:
-288 = -312 * cosA
Dividing both sides by -312:
cosA = -288 / -312
cosA ≈ 0.923
Using the inverse cosine function, we can find angle A:
A = cos^(-1)(0.923)
A ≈ 22.6
Rounding to the nearest whole number, we have A ≈ 23.
Therefore, angle A in the right triangle is approximately 23 degrees.