a) use the sine law to find angle A
sinA/8 = sin 120°/12
sinA = .57735..
angle A = appr 35.3° and angle C = appr 24.7° <----- b iii)
b i) make your sketch and see that
perp. height/12 = sin C
perp.height = 12 sin 24.7 = appr 5.02
ii) area of triangle = (1/2)(12)(8)sin24.7° = ....
iii) see above
The given data is often called the ambiguous case and often results in two different
answers if the sine law is use. However since we can have only one obtuse angle in a triangle
and one angle was 120°, we don't have to worry about that situation.
In a triangle ABC, BC = 8 cm and AC = 12 cm and angle ABC = 120.
a. Calculate the length of AB, correct to one decimal place.
b. If BC is the base of the triangle, calculate, correct to one decimal place;
(i) the perpendicular height of triangle;
(ii) the area of the triangle;
(iii) the size of angle ACB.
1 answer