Cosine Rule trigonometry Question

Question

Do the following question twice, once using Pythagoras and the cosine rule and once using right triangle trigonometry.

Find, to the nearest degree, the size of the largest of the 3 angles of ΔABC where A, B and C have coordinates A (6,2), B (2,5), C (-6,-3)

Answer 1

(6,2), (2,5), (-6,-3)

have sides of lengths

5, 13 and 8sqr2 = about 8(1.414) = about 11.31

13 is largest side, and the opposite angle is also largest angle

13^2 =25+ 128 - 2(5)(8sqr2)cosC

solve for C = about 98.18 degrees

= 98

rounded to nearest degree

had the sides been 5, 12, 13 it would have been a Pythagorean triple with a right triangle, and largest angle = 90

Answer 2

1) Plot points

2) Determine length of AB, BC, and CA

3) Largest angle is opposite longest side

4) Use Law of Cosines to determine size of largest angle.

Questions?