Question

A)
Use the Law of Cosines,
, to find the value of angle
in a right triangle,where
,
, and
.
(1 point)
a2 = b2 + c2 − 2bc ⋅ cosA A
a = 12 b = 35 c = 37
42.1 degrees
71.0 degrees
89.9 degrees
18.9 degrees
A)
If oblique
has side
in., side
in., and included
, then what is thelength of side
a
?
(1 point)
ΔABC b = 32 c = 45 ∠A = 56°
1,439 in.
49 in.
38 in.
2,440 in.

Answer 1

1) Use Law of Cosines solved for cos A:
cos A = (b^2 + c^2 − a^2) / (2bc) = (35^2 + 37^2 − 12^2) / (2·35·37)
= 2450 / 2590 ≈ 0.94672 → A ≈ cos⁻¹(0.94672) ≈ 18.9°

Answer: 18.9 degrees

2) Use Law of Cosines to find a:
a^2 = b^2 + c^2 − 2bc cos A = 32^2 + 45^2 − 2(32)(45)cos56°
= 1024 + 2025 − 2880·cos56° ≈ 3049 − 1610.48 ≈ 1438.52
a ≈ √1438.52 ≈ 37.93 ≈ 38 in.

Answer: 38 in.