53. By the law of cosines, a2 = b2 + c2 - 2bc cos∠A for a triangle with sides of lengths a, b, and c opposite ∠A, ∠B, and ∠C, respectively. A boat travels 25 miles due east, makes a 40° turn toward the north, and then travels 30 miles, as shown below. To the nearest mile, what is the straight-line distance between the boat's starting position and its ending position?
(Note: cos 40° ≈ 0.766, cos(180-α) = -cos α)
Your Answer is
Correct Answer is B
Explanation
From the question, we can know that the angle between the two points is 180° - 40° = 140°. Put 25, 30, and 140° into the formula a2 =b2 sup> + c2 - b, c and ∠A in 2bccos∠A can get a2 = 625 + 900 - 2 ×25 × 30 × cos140° = 2674 , a=51.7≈52, so choose B