Answer:
A. 48.35°, 94.94°, 36.71°
Step-by-step explanation:
Given,
ABC is a triangle,
In which AB = 12 miles, BC = 15 miles and AC = 20 miles,
By the cosine law,
[tex]BC^2 = AC^2 +AB^2 -2\times AC\times AB\times cos A[/tex]
[tex]2(AC)(AB)cos A=AC^2+AB^2-BC^2[/tex]
[tex]\implies cos A = \frac{AC^2+AB^2-BC^2}{2(AC)(AB)}----(1)[/tex]
Similarly,
[tex]cos B = \frac{BC^2+AB^2-AC^2}{2(BC)(AB)}----(2)[/tex]
[tex]cos C = \frac{BC^2+AC^2-AB^2}{2(AC)(BC)}----(3)[/tex]
By substituting the values in equation (1),
[tex]cos A=\frac{20^2+12^2-15^2}{2(20(12)}=0.66458[/tex]
[tex]\implies m\angle A\approx 48.35^{\circ}[/tex]
Similarly, from equation (2) and (3),
[tex]m\angle B\approx 94.94^{\circ}[/tex]
[tex]m\angle C\approx 36.71^{\circ}[/tex]
Hence, Option 'A' is correct.
