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The four cases in which we can solve a triangle are $$ASA SSA SAS SSS$$ (a) In which of these cases can we use the Law of sines to solve the triangle? (b) Which of the cases listed can lead to more than one solution (the ambiguous case)?

Find the reference angle for the given angle. (a) \(99^{\circ}\) (b) \(-199^{\circ}\) (c) \(359^{\circ}\)

Find the exact value of the trigonometric function. $$\cos 660^{\circ}$$

Tracking a Satellite The path of a satellite orbiting the earth causes the satellite to pass directly over two tracking stations \(A\) and \(B,\) which are 50 mi apart. When the satellite is on one side of the two stations, the angles of elevation at \(A\) and \(B\) are measured to be \(87.0^{\circ}\) and \(84.2^{\circ},\) respectively. (a) How far is the satellite from station \(A ?\) (b) How high is the satellite above the ground? (Image can't copy)

Distance Across a River To find the distance across a river, a surveyor chooses points \(A\) and \(B\), which are 200 ft apart on one side of the river (see the figure). She then chooses a reference point \(C\) on the opposite side of the river and finds that \(\angle B A C=82^{\circ}\) and \(\angle A B C \approx 52^{\circ} .\) Approximate the distance from \(A\) to \(C\). (Image can't copy)

The Leaning Tower of Pisa The bell tower of the cathedral in Pisa, Italy, leans \(5.6^{\circ}\) from the vertical. A tourist stands \(105 \mathrm{m}\) from its base, with the tower leaning directly toward her. She measures the angle of elevation to the top of the tower to be \(29.2^{\circ} .\) Find the length of the tower to the nearest meter.

Soap Bubbles When two bubbles cling together in midair, their common surface is part of a sphere whose center \(D\) lies on the line passing through the centers of the bubbles (see the figure). Also, \(\angle A C B\) and \(\angle A C D\) each have measure \(60^{\circ} .\) (a) Show that the radius \(r\) of the common face is given by $$ r=\frac{a b}{a-b} $$ [Hint: Use the Law of Sines together with the fact that an angle \(\theta\) and its supplement \(180^{\circ}-\theta\) have the same sine.] (b) Find the radius of the common face if the radii of the bubbles are \(4 \mathrm{cm}\) and \(3 \mathrm{cm} .\) (c) What shape does the common face take if the two bubbles have equal radii? (Image can't copy)

Find an angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal with the given angle. $$-100^{\circ}$$

A fisherman leaves his home port and heads in the direction \(\mathrm{N} 70^{\circ} \mathrm{W}\). He travels \(30 \mathrm{mi}\) and reaches Egg Island. The next day he sails \(N 10^{\circ} \mathrm{E}\) for \(50 \mathrm{mi}\), reaching Forrest Island. (a) Find the distance between the fisherman's home port and Forrest Island. (b) Find the bearing from Forrest Island back to his home port.] (GRAPH CAN'T COPY)

A 125-ft tower is located on the side of a mountain that is inclined \(32^{\circ}\) to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (IMAGE CAN'T COPY)