solve for the requested variable based on the given information. round your answers to the nearest…

solve for the requested variable based on the given information. round your answers to the nearest hundredth\n39. a = 38°, b = 10, solve for c\n40. b = 88°, b = 2, solve for a\n41. a = 44°, c = 12, solve for b\n42. b = 71°, a = 18, solve for c
Answer
Explanation:
Step1: Recall cosine function in right - triangle
In right - triangle (ABC) with right - angle at (C), (\cos A=\frac{b}{c}).
Step2: Rearrange formula to solve for (c)
Given (A = 44^{\circ}) and (b = 10), from (\cos A=\frac{b}{c}), we can rewrite it as (c=\frac{b}{\cos A}).
Step3: Substitute values
(c=\frac{10}{\cos44^{\circ}}). Since (\cos44^{\circ}\approx0.7193), then (c=\frac{10}{0.7193}\approx13.90).
Answer:
(c\approx13.90)