Question
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
16.3 degrees
16.3 degrees
89.9 degrees
89.9 degrees
73.6 degrees
73.6 degrees
25.1 degrees
Answers
GPT 3.5
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.
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.