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

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

3. 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 =
102
Which formula should we use?
Area = ½ ac sin B
Area = ½ (90)(52) sin 102

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

5. 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.

6. 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

7. Reading Bearings Bearing to A: N 70° E Bearing to B: N 40° WC 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

8. 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

9. 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

10. 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?

11. C A B 3) Find the height? Find angle C63 A B
Find angle C
Use law of sines to find the height.
15.3 m

12. 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.

13. 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.

14. 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

15. 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

16. 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

17. HW: finish the WS