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
16.3 degrees
16.3 degrees
89.9 degrees
89.9 degrees
73.6 degrees
73.6 degrees
25.1 degrees
To solve for angle A using the Law of Cosines, we can rearrange the formula as:
cos A = (b^2 + c^2 - a^2) / (2bc)
Substituting the given values, we have:
cos A = (24^2 + 25^2 - 7^2) / (2 * 24 * 25)
cos A = (576 + 625 - 49) / (48 * 25)
cos A = 1152 / 1200
cos A = 0.96
Taking the inverse cosine of 0.96, we find:
A = cos^(-1) (0.96)
A ≈ 16.3 degrees
Therefore, the answer is 16.3 degrees.