Check my answer for a trig question?

which value best approximates the length of c in triangle abc where c=90°, b=12, and b=15°?

a. c≈3.1058
b. c≈12.4233 (my answer)
c. c≈44.7846
d. c≈46.3644

Aquality characteristic of new iphone x made at the amsterdam plant at apple computers has a manufacturing specification (in mm) of 0.200 +/- .07. historical data indicates that if the quality characteristic takes on values greater than 0.27 or smaller than 0.13 the component fails at a cost of20.19. based on these data: determine the taguchi loss function (must show work) calculate an estimated loss for a quality characteristic of .30 calculate an estimated loss for quality characteristic of .40.

The 40th parallel of north latitude runs across the united states through philadelphia, indianapolis, and denver. at this latitude, earth’s radius is about 3030 miles. the earth rotates with an angular velocity of latex: \frac{\pi}{12} π 12 radians (or 15°) per hour toward the east. if a jet flies due west with the same angular velocity relative to the ground at the equinox, the sun as viewed from the jet will stop in the sky. how fast in miles per hour would the jet have to travel west at the 40th parallel for this to happen? show your work and explain your process.

Which of the following illustrates the product rule for logarithmic equations? a. log2(4x)=log24/log2x b. log2(4x)=log24xlog2x c. log2(4x)=log24-log2x d. log2(4x)=log24+log2x