Answer:
Part A
The distance from the start point the goose travels is approximately 84.96 miles
Part B
The direction the goose travel is approximately 71° Northeast
Explanation:
Part A
The distances the goose flies is given as follows;
The distance directly 45 degrees southeast the goose travels, AB = 55 miles
The distance Northeast the goose travels, BC = 75 miles
The angle Northeast the goose travels = 35°
From the attached drawing of the path the goose travels, we have, by cosine rule, the following relation;
a² = b² + c² - 2·b·c·cos(A)
Therefore, we have;
The length of side ² = 55² + 75² - 2 × 55 × 75 × cos(80°) = 7217.40253425
= √(7217.40253425) ≈ 84.9552972701
The distance from the start point the goose travels ≈ 84.96 miles
Part B
By sine rule, we have;
75/(sin(A)) = /(sin(80°))
sin(A) = (75/) × (sin(80°)
∴ sin(A) = (75/84.9552972701) × (sin(80°) = 0.8694052016
∠A = arcsin(0.8694052016) = 60.3895991264° ≈ 60.4°
The direction the goose travel = 180 - 64 - 45 = 71°
∴ The direction the goose travel =≈ 71° Northeast
