A pilot is flying over a straight highway He determines the

A pilot is flying over a straight highway. He determines the angles or depression to two mileposts, 6 mi apart, to be x = 35 degree and y = 45 degree, as shown in the figure. (Round your answers to two decimal places.) (a) Find the distance of the plane from point A. 4.51 mi (b) Find the elevation of the plane. 7.86 mi To find the distance across a river, a surveyor chooses points A and B, which are x = 150 ft apart on one side of the river (see the figure). She then chooses a reference point C on the opposite side of the river and finds that BAC = 82 degree and ABC = 52 degree. Approximate the distance from A to C. (Round your answer to the nearest foot.)

Solution

Solution:

(a)

Let P be the point where the plane is currently located. The length of AP is the same as the value of b (as shown in the diagram).

Notice how the angle of depression corresponds to the congruent angle of elevation. Also I got the 100° from the fact that 180° - 35° - 45° = 100°

Use the law of sines to solve for b

=> b / sin(45°) = 6 / sin(100°)

=> b = sin(45°) * 6 / sin(100°)

=> b = 4.31 mi

(b)

Using trig, we know;

sine = opposite / hypotense

sin(35°) = h/b

Sin(35°) = h / (4.31)

h = 4.31 * Sin(35°)

h = 2.47 mi