In triangle ABC, ∠A = 35°, a = 16, and b = 21.
(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 ∆ABC / area of ∆A1B1C1 = sin(C) / sin(C1).
By the area formula, we see the following.
Area of ∆ABC / Area of ∆A1B1C1 = (1/2 ab sin(C)) / (1/2 ab sin(C1)) = sin(C) csc(C1)