Question

Select the correct answer.

Answer 1

Answer: B, 35.41, 67.87, and 76.72

Answer 2

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,

$BC^2 = AC^2 +AB^2 -2\times AC\times AB\times cos A$

$2(AC)(AB)cos A=AC^2+AB^2-BC^2$

$\implies cos A = \frac{AC^2+AB^2-BC^2}{2(AC)(AB)}----(1)$

Similarly,

$cos B = \frac{BC^2+AB^2-AC^2}{2(BC)(AB)}----(2)$

$cos C = \frac{BC^2+AC^2-AB^2}{2(AC)(BC)}----(3)$

By substituting the values in equation (1),

$cos A=\frac{20^2+12^2-15^2}{2(20(12)}=0.66458$

$\implies m\angle A\approx 48.35^{\circ}$

Similarly, from equation (2) and (3),

$m\angle B\approx 94.94^{\circ}$

$m\angle C\approx 36.71^{\circ}$

Hence, Option 'A' is correct.