Objectives Solve oblique triangles using Law of Sines
* Objectives: -Solve oblique triangles using Law of Sines and Law of Cosines -Find areas of oblique triangles.
* -Triangles that are not right triangles
* When the 3 measurements provided fit one of these cases: * Two angles and a nonincluded side (AAS) * Two angles and the included side (ASA) * Two sides and the included angle (SSA) * *choose any 2 ratios to create a proportion with 3 known measurements, and 1 unknown.
* A) Solve ΔLMN. Round side lengths to the nearest tenth and angle measures to the nearest degree.
* B) Solve for y in ΔXYZ. Round side lengths to the nearest tenth.
* A) The angle of elevation from the top of a building to a hot air balloon is 62º. The angle of elevation to the hot air balloon from the top of a second building that is 650 feet due east is 49º. Find the distance from the hot air balloon to each building.
* B) A tree is leaning 10° past vertical as shown in the figure. A wire that makes a 42° angle with the ground 10 feet from the base of the tree is attached to the top of the tree. How tall is the tree?
* You know that the measures of two sides and a nonincluded angle (SSA) do not necessarily define a unique triangle. Consider the angle and side measures given in the figures below. In general, given an SSA case, one of the following will be true: * No triangle exists (no solution) * Exactly 1 triangle exists (one solution) * Two triangles exist (two solutions)
SSA v. It is possible for more than 1 triangle to exist, or NO triangle to exist. It all depends on if the given angle is acute or obtuse. v. Always look for 2 triangles when finding an angle using Law of Sines. vhttps: //www. youtube. com/watch? v=Io 3 x. ZMOr bk. Q vvideo
* Given an Obtuse *if OPP ADJ, then NO ∆ exists *if OPP > ADJ, then ONE ∆ exists Given an Acute *if ADJsin( ) > OPP, then NO ∆ exists *if ADJsin( ) = OPP, then ONE ∆ exists *if OPP > ADJ, then ONE ∆ exists *if ADJsin( ) < OPP < ADJ, then TWO ∆s exist
* 1. Using the FIRST angle you found, subtract this number from 180º. This is the 2 nd degree measure for the same angle. 2. The ORIGINAL angle given in the problem, will never change, so take this angle AND the angle from step 1 and subtract them from 180º. (Since all 3 angles have to add up to 180º. ) 3. Use Law of Sines with your new angles to find the remaining side.
* A) Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. m A = 63°, a = 18, b = 25
* B) Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. m C = 105°, b = 55, c = 73,
* A) Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. m B = 45°, b = 18, and c = 24.
* B) Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. m C = 24°, c = 13, and a = 15.
* When the 3 measurements provided fit one of these cases: * Three sides (SSS) * Two sides and the included angle (SAS)
* A) A triangular area of lawn has a sprinkler located at each vertex. If the sides of the lawn are a = 19 feet, b = 24. 3 feet, and c = 21. 8 feet, what angle of sweep should each sprinkler be set to cover?
* B) A triangular lot has sides of 120 feet, 186 feet, and 147 feet. Find the angle across from the shortest side.
* *In SSS, you must find the LARGEST angle first, then use the Law of Sines to find the SMALLER of the 2 remaining angles. *In SAS, you must first find the side across from the known angle, then use the Law of Sines to find the SMALLER of the 2 remaining angles.
* A) Solve ΔABC. Round side lengths to the nearest tenth and angle measures to the nearest degree.
* B) Solve ΔMNP if m M = 54 o, n = 17, and p = 12. Round side lengths to the nearest tenth and angle measures to the nearest degree.
* C) Solve ΔABC. Round angle measures to the nearest degree.
* *Use for SSS*
* A) Find the area of ΔABC to the nearest tenth.
* B) Find the area of ΔGHJ to the nearest tenth.
* A) Find the area of ΔABC to the nearest tenth.
* B) Find the area of ΔDEF to the nearest tenth.
- Slides: 28