Chapter 8

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$A=44^{\circ}, B=22^{\circ}, a=6$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$A=40^{\circ}, b=10, c=7$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(2,3)$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$B=40^{\circ}, a=12, c=20$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(4,-2)$$

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$A=110^{\circ}, C=40^{\circ}, a=12$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$C=118^{\circ}, a=6, b=12$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(-3,7)$$

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$A=105^{\circ}, B=27^{\circ}, b=10$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$C=52.5^{\circ}, a=6.5, b=9$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(\sqrt{2}, \sqrt{3})$$

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$B=42^{\circ}, C=52^{\circ}, b=6$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$A=140^{\circ}, b=12, c=14$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(-3,-\sqrt{2})$$

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$A=67^{\circ}, C=28^{\circ}, a=9$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$B=25.4^{\circ}, a=6.8, c=10.5$$

Evaluate the trigonometric functions at the angle (in standard position) whose terminal side contains the given point. $$(3,-5)$$

Standard notation for triangle ABC is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve triangle ABC under the given conditions. $$A=102.3^{\circ}, B=36.2^{\circ}, a=16$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$C=78.6^{\circ}, a=12.1, b=20.3$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$A=118.2^{\circ}, b=16.5, c=10.7$$

The surveyor in Example 4 stands at the edge of another ravine, which is known to be 115 feet wide. She notes that the angle of depression from the edge she is standing on to the bottom of the oposite side is \(64.3^{\circ} .\) How deep is this ravine?

Solve the triangle. The Law of Cosines may be needed. $$b=12, c=20, B=70^{\circ}$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=7, b=3, c=5$$

Solve the triangle. The Law of Cosines may be needed. $$b=30, c=50, C=60^{\circ}$$

Solve the triangle. The Law of Cosines may be needed. $$a=15, b=12, B=20^{\circ}$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=16, b=30, c=32$$

A 20 -foot-long ladder leans on a wall of a building. The foot of the ladder makes an angle of \(50^{\circ}\) with the ground.How far above the ground does the top of the ladder touch the wall?

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=5.3, b=7.2, c=10$$

Solve the triangle. The Law of Cosines may be needed. $$a=5, c=12, A=102^{\circ}$$

A straight road leads from an ocean beach into the nearby hills. The road has a constant upward grade of \(3^{\circ} .\) After taking this road for one mile, how high above sea level (in feet) are you?(GRAPH CAN'T COPY)

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=7.2, b=6.5, c=11$$

Solve the triangle. The Law of Cosines may be needed. $$a=9, b=14, B=95^{\circ}$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=6.8, b=12.4, c=15.1$$

Solve the triangle. The Law of Cosines may be needed. $$b=12, c=10, C=56^{\circ}$$

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=12, b=16.5, c=20.6$$

Solve the triangle. The Law of Cosines may be needed. $$a=12.4, c=6.2, A=72^{\circ}$$

A wire from the top of a TV tower to the ground makes an angle of \(49.5^{\circ}\) with the ground and touches ground 225 feet from the base of the tower. How high is the tower?

Directions: Standard notation for triangle \(A B C\) is used throughout. Use a calculator and round off your answers to one decimal place at the end of the computation. Solve the triangle ABC under the given conditions. $$a=5.7, b=20.4, c=16.8$$

Find the angles of the triangle whose vertices are (0,0) (5,-2),(1,-4)

Solve the triangle. The Law of Cosines may be needed. $$a=30, b=40, A=30^{\circ}$$

The Seattle Space Needle casts a 225 -foot-long shadow. If the angle of elevation from the tip of the shadow to the top of the Space Needle is \(69.6^{\circ},\) how high is the Space Needle?

Solve the triangle. The Law of Cosines may be needed. $$b=4, c=10, A=75^{\circ}$$

In Example \(4,\) suppose that the angle between the two tracks is \(112^{\circ}\) and that the average speeds are 90 kilometers per hour for the first train and 55 kilometers per hour for the second train. How far apart are the trains after two hours and 45 minutes?

Solve the triangle. The Law of Cosines may be needed. $$a=50, c=80, C=45^{\circ}$$

From the top of a 130 -foot-high lighthouse, the angle of depression to a boat in Lake Erie is \(2.5^{\circ} .\) How far is the boat from the lighthouse?

Solve the triangle. The Law of Cosines may be needed. $$a=6, b=12, c=16$$

Alice is flying a kite. Her hand is three feet above ground level and is holding the end of a 300 -foot-long kite string, which makes an angle of \(57^{\circ}\) with the horizontal. How high is the kite above the ground?

Solve the triangle. The Law of Cosines may be needed. $$a=16.5, b=18.2, C=47^{\circ}$$

It is claimed that the Ohio Turnpike never has an uphill grade of more than \(3^{\circ} .\) How long must a straight uphill segment of the road be to allow a vertical rise of 450 feet?

Solve the triangle. The Law of Cosines may be needed. $$a=21, c=15.8, B=71^{\circ}$$