Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Aim: What to do, What to do?!? So many formulas!! Where do we begin? Do Now: Regents Question How many distinct triangles can be forms if  A = 30 o, side b = 12 and a = 8? 1) 1 2) 2 3) 3 4) 0

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. x i 2i 3i 4i 5i -4i -3i -2i -i -5i -6i yi Adding Complex Numbers Graphically (2 + 3i) (2 + 3i) + (3 + 0i) (3 + 0i) (5 + 3i) = (2 + 3) + (3i + 0i) = = 5 + 3i vector: 2 + 3i vector: 3 + 0i vector: 5 + 3i

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Adding Vectors Vector - a directed line segment that represents directed force notation: OS R The vectors that represent the applied forces form two adjacent sides of a parallelogram, and the vector that represents the resultant force is the diagonal of this parallelogram. O PS resultant force

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. The Laws! Law of Cosines: Law of Sines: Law of Cosines: A = 1/2 ab sinCArea of Triangle:

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. General Guidelines Law of Sines: Use the Law of Sines when the known information involves ASA, AAS, or SSA. Law of Cosines: Use the Law of Cosines when the known information involves SAS or SSS.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem To determine the distance between 2 points, A and B, on opposite sides of a swampy region, a surveyor chose a point C that was 350 meters from point A and 400 meters from point B. If the measure of  ACB was found to be 105º40’, find to the nearest meter, the distance, AB, across the swampy region. Given 2 sides & included angle: Substitute and solve: A B C º40’ AB 2 = AB = AB = 598 to nearest meter Draw: Law of Cosines

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem A surveyor on the ground takes two readings of the angle of elevation of the top of a tower. From 150’ apart, the measures are 50 o and 70 o. Find the tower’s height to the nearest foot. 150’ 70 o 50 o h B D A C Find AD in ΔABD using Law of Sines; then work in ΔADC for find AC. AC  316’

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem PA and PB are tangent to circle O at points A and B respectively. If PA = 10 cm and m  P = 34 o, find the length of chord AB to the nearest centimeter. B P A o Tangents to a circle from an external point are congruent, making PB = 10. With SAS known, use Law of Cosines. AB  6 cm.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem A canoe race is to be run over a triangular course marked by buoys A, B, and C. The distance between A and B is 100 yards, that between B and C is 160 yards, and that between C and A is 220 yards. Find to the nearest degree, the m  ABC.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem A diagonal of a parallelogram is 50 centimeters long and makes angles of 37 o 10’ and 49 o 20’, respectively, with the sides. Find the length of the shorter side of the parallelogram to the nearest centimeter.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Regents Question – 4 points In triangle ABC, m  A = 40 and m  B = 56. The longest side of the triangle is 36 cm. Find the length of the shortest side to the nearest tenth of a centimeter.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem A vertical transmitting tower AB is located on a slope that is inclined 15 o to the horizontal. At a point C, 80 feet down the slope from the foot of the tower, the tower subtends an angle of 40 o 10’. Find to the nearest foot the height of the tower. 15 o h 80’ 40 o 10’

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Regents Question In triangle DEF, side e = 10, f = 8 and m  D = 110. Find the length of the third side to the nearest tenth. 1) ) ) ) 10.5

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem A surveyor at point P sights two points X and Y that are on opposite sides of a lake. If P is 200 m. from X and 350 m. from Y, and m  XPY = 40, find the distance from X to Y to the nearest meter.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem Some nylon fabric will be cut to cover the kite frame shown below. Diagonal AC is 29 inches. What size should the angles be at A, B, C, and D? B D C A 16 in. 26 in. 16 in. 26 in.

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Model Problem Two forces act on a body at an angle of 72 o, resulting in a force whose magnitude is 110 lb. If the magnitude of one of the original forces is 80 lb., find the magnitude of the other to the nearest pound. 110 lb. 80 lb. 108 o 72 o Draw a parallelogram of forces. A B CD Opposite sides are congruent: AD = BC = 80 Consecutive angles are supplementary: m  ABC = 108 o With SSA known in ΔABC, apply Law of Sines. To find AB, you must know m  ACB. 80 lb. 54 lb. ?

Aim: Using Appropriate Formulas Course: Alg. 2 & Trig. Regents Questions – 6 points The magnitude of the resultant of two forces acting on a body is 90 lbs. The angles between the forces and the resultant are ’ and 56 o 45’. Find the magnitude of the larger force to the nearest tenth of a pound.