Sine Law and Cosine Law Word Problems

A pole tilts toward the sun at an 8-degree angle from the vertical and it casts a 22-foot shadow. The angle of elevation from the base to the top of the pole is 43 degrees. How tall is the pole?

• 39 feet

• 24 feet

• 22 feet

• 20 feet

On a hill inclined at an angle of 14.2 degrees with the horizontal, stands a vertical tower. At a point P, 62.5 meters down the hill from the foot of the tower, the angle of elevation of the top of the tower is 43.6 degrees. How tall is the tower?

• 42 meters

• 49 meters

• 52 meters

• 59 meters

A triangular parcel of land with vertices at R, S, and T was to be enclosed by a fence, but it was discovered that the surveyor’s mark S was missing. From a deed to a property, it was learned that the distance from T to R is 324 meters, the distance from T to S is 506 meters, and the angle at R in the triangle is 125.4 degrees. Determine the location of S by finding the distance from R to S.

• 205 meters

• 211 meters

• 222 meters

• 244 meters

To approximate the length of a marsh, a surveyor walks 250 meters from point A to point B then turns 75 degrees and walks 220 meters to point C as shown. Approximate the length AC of the marsh.

• 373 m

• 360 m

• 353 m

• 303 m

To determine the distance between two aircrafts, a tracking station continuously tracks the distance to each aircraft and the angle A between them as shown. Determine the distance a between the planes when the measure of angle A is equal to 42 degrees, b = 35 miles, and c = 20 miles.

• 18 miles

• 24 miles

• 28 miles

• 32 miles