April 5th copyright2009merrydavidson Calculator today Happy Birthday to: Emily Besserer 9/4 Stephen Hodges 6/8

AREA FORMULA for oblique triangles Heron’s Formula: Memorize these…….. Why use one formula over the other?

Which formula should we use? Area = ½ ac sin B 1) Find the area for a triangular lot having two sides of lengths 90 meters and 52 meters and the included angle of 1020. a = b = c = A = B = C = 90 52 102 Which formula should we use? Area = ½ ac sin B Area = ½ (90)(52) sin 102

2) Find the area for a triangle having sides of 5, 7 and 10. b = c = A = B = C = 5 10 7 Which formula should we use?

Review of Bearings We use bearings to describe the direction something is traveling or the direction in which we see something. A bearing measures the acute angle that a path or line of sight makes with a fixed north/south line.

Reading Bearings Many directions are given using a combination of two cardinal headings and degree number North (N) and South (S) are always first Then the number of degrees Finally the East (E) or West (W) heading Example: N 53° W

Reading Bearings Bearing to A: N 70° E Bearing to B: N 40° W C D O 40º 75º 25º 20º Bearing to A: N 70° E Bearing to B: N 40° W Bearing to C: S 15° W Bearing to D: S 25° E

Example 3 A boat leaves the entrance of a harbor and travels 40 miles on a bearing of S64E. How many miles south and east did the has the boat traveled? S64E 40 miles a b

Alternate Bearing Method Problems may just give you a single bearing 130 degrees This is always referenced from North clockwise to the bearing (heading). N 130

Now application of oblique triangles. 3) Due to winds a tree grew so it was leaning 4 degrees from vertical. At a point 35 meters from the tree, the angle of elevation to the top of the tree is 23 degrees. Find the height?

C A B 3) Find the height? Find angle C 63 A B Find angle C Use law of sines to find the height. 15.3 m

4) A plane flies 500 kilometers at a bearing of 316 degrees from Naples to Elgin. The plane then flies 720 kilometers to Canton (due west of Naples). Find the bearing of the flight from Elgin to Canton? Draw in little compass lines at the vertices.

B A C 44 44 46 Complementary angles gives you 460 Looking for this B 44 44 46 A C Complementary angles gives you 460 Alternate interior angles gives you 440 Find angle B and subtract 440 for the bearing.

B 44 44 46 A C a = 500 b = c = 720 A = B = ? C = 46 Find angle A using law of sines S600W or 2400 104 What is the bearing from Elgin to Canton? 30

3) A boat race runs along a triangular course marked with buoys A, B, and C. The race starts with boats headed west for 3700 meters. The other two sides of the course lie to the north of the first side and their lengths are 1700 meters and 3000 meters. Draw a visual picture of the course and then find the bearings for the final two legs of the race. C 1700 meters 3000 meters B A 3700 meters

C B A S 63.1o E N 37.1o E C is the largest angle, find this First. Store it! a = 1700 b = 3000 c = 3700 A = B = C = What is the bearing from C to A? S 63.1o E 52.9 100.2 Now find angle B using law of sines What is the bearing from B to C? N 37.1o E Looking for this What is this angle? C 1700 meters 3000 meters 52.9 B A 3700 meters

HW: finish the WS