Question

In Exercises 17–32, two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round to the nearest tenth and the nearest degree for sides and angles, respectively.
a = 7, b = 28, A = 12°

Accepted Answer

Identify the given elements: side $$a = 7$$, side $$b = 28$$, and angle $$A = 12^\circ. $$Since we have two sides and a non-included angle (SSA), this is the ambiguous case in triangle solving. Calculate the height $$h of $$the triangle using the formula $$h = b 	imes \sin A. $$This height helps determine how many triangles can be formed. Compare side $$a$$ with the height $$h$$ and side $$b to $$determine the number of possible triangles: if $$a \u003c h$$, no triangle; if $$a = h$$, one right triangle; if $$h \u003c a \u003c b$$, two triangles; if $$a \geq b$$, one triangle. If one or two triangles are possible, use the Law of Sines to find angle $$B by $$solving $$\sin B = \frac{b \sin A}{a}. $$Remember to consider the possible ambiguous angle $$B' if $$two triangles exist. After finding angle(s) $$B$$, calculate angle $$C$$ using $$C = 180^\circ - A - B (or$$ $$B'$$), then use the Law of Sines again to find side $$c$$ for each triangle. Round all answers to the nearest tenth for sides and nearest degree for angles.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Law of Sines

Ambiguous Case (SSA) in Triangle Solutions

Triangle Inequality and Angle-Side Relationships