SINE AND COSINE LAW



Recall: If your distance from the foot of the tower is 20 m and the angle of elevation is 40°, find the height of the tower.2571750163195Find angle XThe Sine and Cosine Laws are used to solve triangles that are not right triangles.10287025336500For?ABC: A The Sine Law states: sinAa=sinBb=sinCcOR-147955181306B00B1389380135255C00C The Law of Cosines states: a2=b2+c2-2bccosA b2= c2=Example 1Find the length of the indicated side.a) In ?ABC: A=63°, B=32°, a=12.4 cm, find b.17272010795000b) In ?DEF: D=80°, e=10.2 m, f=12.4 m. Find d. 26606514287500Example 2Find the indicated angle:a) In ?ABC: a=3.3 cm, b=4.2 cm, c=5.1 cm. Determine the measure of A.20701017335500b) In ?JKL: J=67°, j=14 m, k=12 m.??Determine the measure of K.2286004318000Example 3A ski lift begins at ground level 0.75 miles from the base of a mountain whose face has a 50° angle of elevation. The ski lift ascends in a straight line at an angle of 20° to the top of the mountain. Find the length of the ski lift from the beginning of the ski lift to the top of the mountain, to the nearest hundredth of a mile.Example 4Carmen and Jamal are standing 5280 ft apart on a straight, horizontal road. They observe a hot-air balloon between them directly above the road. The angle of elevation from Carmen’s eyes is 60° and from Jamal’s eyes is 75°. Carmen and Jamal’s eyes are both at a height of 5.8 ft. Draw a diagram to illustrate this situation, and find the height of the balloon to the nearest foot.Example 5A ship at sea heads directly toward a cliff on the shoreline. A crewman is looking out a window at sea level, and sees an angle of elevation of 30° to the top of the cliff. The boat moves 30 feet closer to the cliff, and now the crewman sees an angle of elevation of 45° to the top of the cliff. What is the height of the cliff to the nearest foot?Example 6A 15 ft tall sign is placed on top of an office building. From a point on the sidewalk level with the base of the building, the angle of elevation to the top of the sign and the angle of elevation to the bottom of the sign are 40° and 32°, respectively. Sketch a diagram to represent the situation. Find the height of the building to the nearest foot.Homework: pg.221 #9-12, pg.254 #1-5,pg.246 #1ac, 8ac,pg. 237 #1b, 2b ................
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