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# Law of sine and cosines

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### Law of sine and cosines

1. 1. Right Triangle Problems, Law of Sines, Law of Cosines & Problem Solving T- 1-855-694-8886 Email- info@iTutor.com By iTutor.com
2. 2. Right Triangle Problems Any situation that includes a right triangle, becomes solvable with trigonometry. Angle of Elevation Angle of Depression © iTutor. 2000-2013. All Rights Reserved
3. 3. This diagram has an inscribed triangle whose hypotenuse is also the diameter of the circle.A B C Given: = 40o, AB = 6 cm Determine the area of the shaded region. Solution: Sin 40o = 6/AC; AC = 6/ sin40o = 9.33 cm AC/2 = radius of the circle = 4.67 cm; BC = 6/tan 40o =7.15 cm Ao = r2 = 68.4 cm2, A = ½bh = 21.5 cm2; A = 46.9 cm2 © iTutor. 2000-2013. All Rights Reserved
4. 4. This diagram has a right triangle within a cone that can be used to solve for the surface area and volume of the cone.h r l Given: = 55o, l = 6 cm Determine the area and volume of the cone. Solution: Sin 55o = h/l; h = 6 x sin55o = 4.91 cm tan 55o = h/r; r = h/ tan 55o = 4.91/ tan 55o = 3.44 cm Acone = r(r + l) = (3.44)(3.44 + 6)cm2; Acone = 102 cm2 Vcone =⅓ r2h = ⅓ (3.44)2(4.91)cm3; Vcone = 60.8 cm3 © iTutor. 2000-2013. All Rights Reserved
5. 5. The angle of elevation of a ship at sea level to a neighboring lighthouse is 2o . The captain knows that the top of lighthouse is 165 ft above sea level. How far is the boat from the lighthouse? h x Solution: tan 2o = h/x; 1 mile = 5280 ft, so the ship is .89 mile away from the lighthouse. x = h/tan 2o x = 165/ tan 2o = 4725 ft; © iTutor. 2000-2013. All Rights Reserved
6. 6. Function Values – Unit Circle The unit circle is a circle with a radius of 1 unit. x y Sin = y; Cos = x; Tan = y/x  The coordinate of P will lead to the value of x and y which in turn leads to the values for sine, cosine, and tangent.  Use the reference angle in each quadrant and the coordinates to solve for the function value. © iTutor. 2000-2013. All Rights Reserved