2. Trigonometric Functions on Right Triangles

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.B = 39°09', c = 0.6231 m

Solve each problem. See Examples 1–4. Distance across a Lake To find the distance RS across a lake, a surveyor lays off length RT = 53.1 m, so that angle T = 32°10' and angle S = 57°50'. Find length RS.

Solve each problem. See Examples 1–4. Diameter of the Sun To determine the diameter of the sun, an astronomer might sight with a transit (a device used by surveyors for measuring angles) first to one edge of the sun and then to the other, estimating that the included angle equals 32'. Assuming that the distance d from Earth to the sun is 92,919,800 mi, approximate the diameter of the sun.

Solve each problem. See Examples 1–4. Altitude of a Triangle Find the altitude of an isosceles triangle having base 184.2 cm if the angle opposite the base is 68°44'.

Solve each problem.See Examples 3 and 4.Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?

Solve each problem.See Examples 3 and 4.Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.

Solve each problem.See Examples 3 and 4.Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

Solve each problem.See Examples 3 and 4.Angle of Elevation of the Sun The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun to the nearest hundredth of a degree.

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.A = 39.72°, b = 38.97 m

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.)Height of a Tower The angle of depression from a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. Find the height of the tower.