In triangle ABC, ∠A = 35°, a = 18, and b = 24.
(a) Show that there are two triangles, ABC and A1B1C1, that satisfy these conditions.
Using the Law of Sines, we know the following. (Round your answers to three decimal places.)
sin(B) ≈
∠B ≈ ° and ∠B1 ≈ 180° − ° ≈ °
For triangle ABC, we see the following. (Round your answers to two decimal places.)
∠C ≈ °
and c ≈
For triangle A1B1C1, we see the following. (Round your answers to two decimal places.)
∠C1 ≈ °
and c ≈
Thus, there are two triangles that satisfy these conditions.
(b) Show that the areas of the triangles in part (a) are proportional to the sines of the angles C and C1, that is,
area of ΔABC / area of ΔA1B1C1 = sin(C) / sin(C1).
By the area formula, we see the following.
Area of ΔABC / Area of ΔA1B1C1 = (1/2 ab sin(C)) / (1/2 ab sin(C1)) =