Warm Up Apr. 30th 1. A 100-foot line is attached to a kite. When the kite has

pulled the line taut, the angle of elevation to the kite is 50°. Find the height of the kite.

2. At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack on top of the building is 35° and the angle of elevation to the top is 53°. Find the height of just the smoke stack.

Homework Questions??

Solving TrianglesDevelop and understand the Law of Sines & Cosines. Use them to solve oblique triangles and applications.

Get your bearings…

Bearing measures the acute angle a path or line of sight makes with a fixed north-south

or east-west line.

For example: S 35 E or W 10 N

Example•An airplane flying at 600 mph has a bearing of S 34 E.

After flying 3 hours, how far south has the plane traveled from its departure?

Oblique Triangles•Triangles without a right angle.

•To solve any oblique triangle, you need to know at least ONE SIDE and any two other parts.▫2 angles, 1 side (ASA or AAS)▫2 sides, angle opposite one of them (SSA)▫3 sides (SSS)▫2 sides and the included angle (SAS)

Law of SinesIf you’re given 2 angles and 1 side (ASA or AAS) use the Law of Sines

Example•Solve the triangle ABC: A = 35o, B = 100o, a = 8

Applications• Tracking station B is located 110 miles east of

station A. A forest fire is located at C, on a bearing N42°E of station A and N15°E of station B. How far is the forest fire from station A?

If you are given • three sides (SSS) or • two sides and the included angle (SAS) then solve use Law of Cosines to start off.

a

b

c

B

AC

Cabbac cos2222

Application•Two planes leave the same airport at the same

time. The first plane is traveling 500 mph bearing W 30ºN. The second plane is bearing N 27º W traveling at 600 mph. How far apart are the planes after 3 hours?

Example•Solve the triangle DEF: d = 8.2, e = 3.7, f = 10.8

You Try!•Solve each triangle:1. ∆ABC: A = 10o, B = 60o, a = 4.52. ∆PQR: p = 21, r = 15, q = 103. ∆JKL: J = 59o, L = 47o, k = 100

4. To approximate the length of a marsh, a surveyor walks 380 meters from point A to B, then turns 80° and walks 240 meters to point C. Approximate the length AC of the marsh.

C

B

A

80°