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 .(1 point)
Responses
25.1 degrees
25.1 degrees
73.6 degrees
73.6 degrees
89.9 degrees
89.9 degrees
16.3 degrees
89.9 degrees
Using the Law of Cosines:
a^2 = b^2 + c^2 - 2bc*cos(A)
7^2 = 24^2 + 25^2 - 2(24)(25)*cos(A)
49 = 576 + 625 - 1200*cos(A)
49 = 1201 - 1200*cos(A)
1200*cos(A) = 1201 - 49
1200*cos(A) = 1152
cos(A) = 1152/1200
cos(A) = 0.96
A = cos^(-1)(0.96)
A ≈ 89.9 degrees
Therefore, angle A ≈ 89.9 degrees.