A boat leaves a dock and travels north-west at a distance of 1,250 ft. A second boat leaves the same dock and travels 1,835 ft in the north-eastern direction. If the two boats are 860ft apart from each other, find the angle between the two boats.

A) 24°

B) 45°

C) 42°

D) 25°

Two observers are 200 meters apart on a straight shoreline, looking at a sailboat out at sea. The angles of elevation from the observers to the boat are 30 degrees and 45 degrees, respectively. Find the distance from the sailboat to each observer.

A) First observer = 164.37 m
Second observer = 103.51 m

B) First observer = 146.37 m
Second observer = 103.51 m

C) First observer = 164.73 m
Second observer = 130.51 m

D) First observer = 103.51 m
Second observer = 146.37 m

In triangle XYZ, angle X measures 50 degrees, side XY measures 10 units, and side YZ measures 12 units. Find the measure of angle Y and side XZ.

A) Y = 76.78° and XY = 8.33 units

B) Y = 66.78° and XY = 8.33 units

C) Y = 86.78° and XY = 8.33 units

D) Y = 66.78° and XY = 6.33 units

Two swimmers jump off a pier and swim in two different directions. The angle between the two swimmers are 85 degrees. Both two swimmers swam a 200 ft. distance. Find the final distance between the two swimmers.

A) 240.7 ft

B) 207.2 ft

C) 204.7 ft

D) 270.2 ft

A tree stands on a slope. From a point 20 in uphill, the angle of elevation to the top of the tree is 30 degrees. From a point 40 in downhill from the same point, the angle of elevation to the top of the tree is 15 degrees. Find the height of the tree.

A) 9.04 in

B) 10.49 in

C) 9.40 in

D) 10.94 in

Solve triangle ABC, given A = 40°, a = 50, b = 30. Find missing angles B and C and side c.

A) c = 69.1, B = 23° and C = 117°

B) c = 68, B = 22.7° and C = 117.3°

C) c = 69.1, B = 22.7° and C = 117.3°

D) c = 68, B = 22.5° and C = 117.5°

In rectangle ABCD, point E lies on side BC such that DE is perpendicular to AB, and DE = 6 m. AB = 12 m and AD = 8 m. Find the length of CE.

A) \$\sqrt(3)\$

B) \$3\sqrt(7)\$

C) \$sqrt(7)\$

D) \$7\sqrt(3)\$

During her shift, a pilot flies from Columbus to Atlanta, a distance of 448 miles, and then on to the Phoenix, a distance of 1583 miles. From Phoenix, she returns home to Columbus, a distance of 1667 miles. Determine the angles of the triangle created by her flight path.

A) 15.6°, 71.5° and 92.9°

B) 15.6°, 71.4° and 92.4°

C) 16°, 71° and 92.9°

D) 15.5°, 71.9° and 92.5°

A quadrilateral ABCD has sides AB = 10 ft, BC = 12 ft, CD = 8 ft, and angle B = 60 degrees. Diagonal AC divides the quadrilateral into triangles ABC and ACD. Find side AC.

A) 12.3 ft

B) 11.13 ft

C) 13.3 ft

D) 14.3 ft

The light from a lighthouse can be seen from an 18-mile radius. A boat is anchored so that it can just see the light from the lighthouse. A second boat is located 25 miles away from the lighthouse and is headed straight toward it, making a 44º angle with the lighthouse and the first boat. Find the distance between the two ships when the second boat enters the radius of the lighthouse light.

A) 13.8 miles

B) 15.8 miles

C) 18.3 miles

D) 19.8 miles