Download Questions over 7.1 and 7.2

Questions over 7.1 and 7.2
Section 7.3
Example: Solve the triangle if A = 43o, b = 25 ft, and c = 20 ft.
Remember the Law of Sines works whenever you are given any two
angles and one side (AAS or ASA)...or...given SSA information (one,
two, or no triangles possible).
What if we are given SAS information?
Oh woe is us...what will we do???
Law of Cosines (SAS)
For the oblique triangle ABC, C
a
b
A
a2 = b2 + c2 ­ 2bc cos A
b2 = a2 + c2 ­ 2ac cos B
c
B
c2 = a2 + b2 ­ 2ab cos C
EXAMPLE: In triangle ABC, if a = 4.2 cm, c = 7.5 cm, and B = 32o, find b. Suppose we are given a = 5 cm, b = 7 cm, and c = 11 cm.
Can we solve the triangle?
If we are given SSS information...
We can use Law of Cosines to solve the triangle in this case.
We must solve for an angle first!
a2 = b2 + c2 ­ 2bc cos A This gives us an alternate statement of the Law of Cosines.
Law of Cosines (SSS)
For the oblique triangle ABC, C
b
A
cos A = b2 + c2 ­ a2 2bc
a
c
B
cos B = a2 + c2 ­ b2 2ac
cos C = a2 + b2 ­ c2 2ab
Always remember...when using cos­1...your calculator is
programmed to give you angles in certain quadrants.
cos­1(positive number between 0 and 1) = acute Q1 angle
cos­1(negative number between ­1 and 0) = obtuse Q2 angle
EXAMPLE: In triangle ABC, if a = 72 m, b = 54 m, and c = 35 m. Solve the triangle. Helpful Hint: In a SSS problem, always find the largest angle FIRST, using the law of cosines. After that you can switch to law of sines.
Interesting Tidbits:
c
a
C
b
a
C
c
b
c
a
C
b
You are on a plane with a heading of 320 degrees, flying at 244 miles per hour. The heading of the wind is 265 degrees at 45 miles per hour. The wind is pushing the plane off course. Luckily you know trigonometry (you're welcome) so you can find the true heading of the plane and its actual speed.
The resultant vector is the black vector. Its length is the actual speed of the plane. It appears to be longer than the blue plane vector, so it appears as though the wind is speeding up the plane. You can find the length by using the law of cosines. The heading angle is θ. If you find angle A first, then you'll be able to find the heading angle. You can find A using the law of sines.