91Ó°ÊÓ

In Exercises 21-30, construct an appropriate triangle to complete the table. \(Function\) sin \(\theta\) \((deg)\) \(30^\circ\) \(\theta\) \((rad)\) \(Function\) \(Value\)

HEIGHT The length of a shadow of a tree is 125 feet when the angle of elevation of the sun is \(33^\circ\). Approximate the height of the tree.

ALTITUDE You observe a plane approaching overhead and assume that its speed is 550 miles per hour. The angle of elevation of the plane is \(16^\circ\) at one time and \(57^\circ\) one minute later. Approximate the altitude of the plane.

ANGLE OF DEPRESSION A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level?

SPEED ENFORCEMENT A police department has setup a speed enforcement zone on a straight length of highway. A patrol car is parked parallel to the zone, 200 feet from one end and 150 feet from the other end (see figure). (a) Find the length \(l\) of the zone and the measures of the angles \(A\) and \(B\) (in degrees). (b) Find the minimum amount of time (in seconds) it takes for a vehicle to pass through the zone without exceeding the posted speed limit of 35 miles per hour.

AIRPLANE ASCENT During takeoff, an airplane's angle of ascent is \(18^\circ\) and its speed is 275 feet per second. (a) Find the plane's altitude after 1 minute. (b) How long will it take the plane to climb to an altitude of 10,000 feet?

In Exercises 31-36, use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. sec \(\theta\) = \(5\) (a) cos \(\theta\) (b) cot \(\theta\) (c) cot \((90^{\circ} - \theta)\) (d) sin \(\theta\)

In Exercises 15-38, sketch the graph of the function. Include two full periods. \(y =\ \dfrac{1}{4} csc(x+\dfrac{\pi}{4})\)

NAVIGATION A ship leaves port at noon and has a bearing of S \(29^\circ\)W. The ship sails at 20 knots. (a) How many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 P.M.? (b) At 6:00 P.M., the ship changes course to due west. Find the ship's bearing and distance from the port of departure at 7:00 P.M.

In Exercises 23-40, use a calculator to evaluate the expression. Round your result to two decimal places. \(tan^{-1}\ (-\frac{95}{7})\)