7/3/ : The Law of Sines Expectation: G1.3.2: Know and use the Law of Sines and the Law of Cosines and use them to solve problems. Find the area of a triangle with sides a and b and included angle θ using the formula Area = (1/2) a b sin θ.
7/3/ : The Law of Sines The Law of Sines For any triangle Δ ABC, with sides of a, b, and c opposite ∠ A, ∠ B and ∠ C respectively:
7/3/ : The Law of Sines 3 Cases of The Law of Sines 1. Acute Triangles 2. Right Triangles 3. Obtuse Triangles
7/3/ : The Law of Sines Proving the Law of Sines Given: Δ ABC is acute Prove:Sin ASin BSin C a c b
7/3/ : The Law of Sines Acute Case: Law of Sines A B C a b c h x y
7/3/ : The Law of Sines Acute Case: Law of Sines A B C a b c g tu
7/3/ : The Law of Sines Solve the triangle below (calculate all unknown measures). 74° A b B
7/3/ : The Law of Sines Solve the triangle below. 60°42° 5 A B C b a
In the figure below, what is the measure of ∠ α, rounded to the nearest whole degree? a. 20° b. 55° c. 70° d. 75° e. 110° 7/3/2015 The Law of Sines ∠α∠α 55°
7/3/ : The Law of Sines Two cars leave the same house at the same time and each is 40 miles away after 1 hour. Car A traveled in the direction of 60° north of east. Car B traveled in the direction of 25° west of north. How far apart (from each other) are the two cars?
7/3/ : The Law of Sines Solve the triangle below. C A 30° 7 B c 12
7/3/ : The Law of Sines Solve the triangle below. A B 7 30° C 12
7/3/ : The Law of Sines What Happened? The Ambiguous Case: A triangle with an angle and 2 nonincluded sides given (SSA) may have 2 different solutions.
7/3/ : The Law of Sines SsA Condition SSA is not a problem if the given angle is opposite the longer of the 2 given sides. This is called SsA. A triangle to be solved is not ambiguous if it satisfies SsA.
7/3/ : The Law of Sines SsA 5 cm 12 cm 110° This is not an ambiguous case!
7/3/ : The Law of Sines SsA 12 cm 5 cm 18° This is an ambiguous case!
7/3/ : The Law of Sines What to Do? What to Do? If the case is ambiguous, use sin α = sin (180 - α ) to determine both possible angle combinations.
7/3/ : The Law of Sines Solve the triangle below. 30° 7 C B A c 12
Yana is planning a triangular garden. He wants to put a fence around it. The length of one side is 30 feet. If the angles at each end of this side are 44° and 58°, find the length of fencing needed to enclose the garden. 7/3/ : The Law of Sines
7/3/ : The Law of Sines Assignment: Pages 658 – 661, # (odds), 33-35, (all).