Question

Consider triangles with the following measurements. If two sides are given, use the law of cosines to find the

measure of the third side. If three sides are given, use the law of cosines to find the measure of the angle between
a and ????.
a. a = 4, ???? = 6, m∠???? = 35°
b. a = 2, ???? = 3, m∠???? = 110°
c. a = 5, ???? = 5, m∠???? = 36°
d. a = 7.5, ???? = 10, m∠???? = 90°
e. a = 4.4, ???? = 6.2, m∠???? = 9°
f. a = 12, ???? = 5, m∠???? = 45°
g. a = 3, ???? = 6, m∠???? = 60°
h. a = 4, ???? = 5, c = 6
i. a = 1, ???? = 1, c = 1
j. a = 7, ???? = 8, c = 3
k. a = 6, ???? = 5.5, c = 6.5
l. a = 8, ???? = 5, c = 1
m. a = 4.6, ???? = 9, c = 11.9

Answer 1

Answers are in explanation part.

Explanation:

Law of Cosines for side c:
`c=√(a^2+b^2-2ab\cos C)`

a) c = 3.561

b) c = 4.136

c) c = 3.09

d) c = 12.5

e) c = 1.978

f) c = 9.173

g) c = 5.196

Law of Cosines for angle C:
`C=cos^(-1)((a^2+b^2-c^2)/(2ab))`

h) C = 82.819°

i) C = 60°

j) C = 21.787°

k) C = 68.676°

l) Sides (8, 5, 1) cannot form a triangle. It is impossible.

m) C = 118.454°