Chapter 4

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A straight 120 -ft culvert is built down a hillside that makes an angle of \(54.0^{\circ}\) with the horizontal. Find the height of the hill.

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(6,8)$$

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(5,12)$$

Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent). A \(60^{\circ}\) angle included between sides of 3 in. and 6 in.

Solve the given problems. Sketch an appropriate figure, unless the figure is given. On level ground, a tree \(12.0 \mathrm{m}\) high has a shadow \(85.0 \mathrm{m}\) long. What is the angle of elevation of the sun?

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(15,8)$$

Draw the given angles. $$60^{\circ}, 120^{\circ},-90^{\circ}$$

Use a protractor to draw the given angle. Measure off 10 units (centimeters are comvenient) along the radius vector. Then measure the corresponding values of \(x\) and \(y\). From these values, determine the trigonometric functions of the angle. $$40^{\circ}$$

Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent). A side of 4 in. included between angles of \(40^{\circ}\) and \(50^{\circ}\)

Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of \(x\) and \(y\). From these values, determine the trigonometric functions of the angle. $$75^{\circ}$$

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(240,70)$$

Draw the given angles. $$330^{\circ},-150^{\circ}, 450^{\circ}$$

Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent). A right triangle with a hypotenuse of \(5 \mathrm{cm}\) and a leg of \(3 \mathrm{cm}\)

Solve the given problems. Sketch an appropriate figure, unless the figure is given. The headlights of an automobile are set such that the beam drops 2.00 in. for each \(25.0 \mathrm{ft}\) in front of the car. What is the angle between the beam and the road?

Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of \(x\) and \(y\). From these values, determine the trigonometric functions of the angle. $$15^{\circ}$$

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(0.09,0.40)$$

Draw the given angles. $$50^{\circ},-120^{\circ},-30^{\circ}$$

Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent). A right triangle with a \(70^{\circ}\) angle between the hypotenuse and a leg of \(5 \mathrm{cm}\)

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(1.1,6.0)$$

Draw the given angles. $$45^{\circ}, 245^{\circ},-250^{\circ}$$

Use a protractor to draw the given angle. Measure off 10 units (centimeters are comvenient) along the radius vector. Then measure the corresponding values of \(x\) and \(y\). From these values, determine the trigonometric functions of the angle. $$53^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. The bottom of the doorway to a building is \(2.65 \mathrm{ft}\) above the ground, and a ramp to the door for the disabled is at an angle of \(6.0^{\circ}\) with the ground. How much longer must the ramp be in order to make the angle \(3.0^{\circ} ?\)

Solve the right triangles with the given parts. Round off results. $$A=77.8^{\circ}, a=6700$$

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(1, \sqrt{15})$$

Determine one positive and one negative coterminal angle for each angle given. $$45^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. On a test flight, during the landing of the space shuttle, the ship was \(325 \mathrm{ft}\) above the end of the landing strip. If it then came in at a constant angle of \(6.5^{\circ}\) with the landing strip, how far from the end of the landing strip did it first touch ground? (A successful reentry required that the angle of reentry be between \(5.1^{\circ}\) and \(7.1^{\circ} .\) )

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(\sqrt{3}, 2)$$

Solve the right triangles with the given parts. Round off results. $$A=18.4^{\circ}, c=0.0897$$

Determine one positive and one negative coterminal angle for each angle given. $$173^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. From a point on the South Rim of the Grand Canyon, it is found that the angle of elevation of a point on the North Rim is \(1.2^{\circ} .\) If the horizontal distance between the points is \(9.8 \mathrm{mi}\), how much higher is the point on the North Rim?

From a point on the South Rim of the Grand Canyon, it is found that the angle of elevation of a point on the North Rim is \(1.2^{\circ} .\) If the horizontal distance between the points is \(9.8 \mathrm{mi},\) how much higher is the point on the North Rim? Solve the given problems. Sketch an appropriate figure, unless the figure is given.

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(7,7)$$

Solve the right triangles with the given parts. Round off results. $$a=150, c=345$$

Determine one positive and one negative coterminal angle for each angle given. $$-150^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. What is the steepest angle between the surface of a board \(3.50 \mathrm{cm}\) thick and a nail \(5.00 \mathrm{cm}\) long if the nail is hammered into the board such that it does not go through?

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(840,130)$$

Solve the right triangles with the given parts. Round off results. $$a=932, c=1240$$

Determine one positive and one negative coterminal angle for each angle given. $$462^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A robot is on the surface of Mars. The angle of depression from a camera in the robot to a rock on the surface of Mars is \(13.33^{\circ} .\) The camera is \(196.0 \mathrm{cm}\) above the surface. How far from the camera is the rock?

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(50,20)$$

Determine one positive and one negative coterminal angle for each angle given. $$430^{\circ} 30^{\prime}$$

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$\left(1, \frac{1}{2}\right)$$

Determine one positive and one negative coterminal angle for each angle given. $$153^{\circ} 47^{\prime}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A rectangular piece of plywood \(4.00 \mathrm{ft}\) by \(8.00 \mathrm{ft}\) is cut from one corner to an opposite corner. What are the angles between edges of the resulting pieces?

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(0.687,0.943)$$

Determine one positive and one negative coterminal angle for each angle given. $$278.1^{\circ}$$

Solve the given problems. Sketch an appropriate figure, unless the figure is given. A guardrail is to be constructed around the top of a circular observation tower. The diameter of the observation area is \(12.3 \mathrm{m}\). If the railing is constructed with 30 equal straight sections, what should be the length of each section?

Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points. For Exercises \(3-14,\) give answers in exact form. For Exercises 15 and \(16,\) the coordinates are approximate. $$(37.65,21.87)$$

Determine one positive and one negative coterminal angle for each angle given. $$-197.6^{\circ}$$

Find the values of the indicated functions. In Exercises \(17-20,\) give answers in exact form. In Exercises \(21-24,\) the values are approximate. Given \(\cos \theta=12 / 13,\) find \(\sin \theta\) and \(\cot \theta\).