Find the missing parts of the triangle.
-$$\begin{array} { l }
\mathrm { A } = 44.29 ^ { \circ } \
\mathrm { a } = 51.82 \mathrm { yd } \
\mathrm { b } = 63.64 \mathrm { yd }
\end{array}$$
If necessary, round angles and side lengths to the nearest hundredth.
A) no such triangle
B) $\mathrm { B } _ { 1 } = 59.04 ^ { \circ } , \mathrm { C } _ { 1 } = 76.67 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 120.96 ^ { \circ } , \mathrm { C } _ { 2 } = 14.75 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$
C) $\mathrm { B } _ { 1 } = 76.67 ^ { \circ } , \mathrm { C } _ { 1 } = 59.04 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$
D) $\mathrm { B } = 59.04 ^ { \circ } , \mathrm { C } = 76.67 ^ { \circ } , \mathrm { c } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 14.75 ^ { \circ } , \mathrm { C } _ { 2 } = 120.96 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$

Question

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { A } = 44.29 ^ { \circ } \
\mathrm { a } = 51.82 \mathrm { yd } \
\mathrm { b } = 63.64 \mathrm { yd }
\end{array}$$
If necessary, round angles and side lengths to the nearest hundredth.
A) no such triangle
B) $\mathrm { B } _ { 1 } = 59.04 ^ { \circ } , \mathrm { C } _ { 1 } = 76.67 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 120.96 ^ { \circ } , \mathrm { C } _ { 2 } = 14.75 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$
C) $\mathrm { B } _ { 1 } = 76.67 ^ { \circ } , \mathrm { C } _ { 1 } = 59.04 ^ { \circ } , \mathrm { c } _ { 1 } = 72.21 \mathrm { yd }$
D) $\mathrm { B } = 59.04 ^ { \circ } , \mathrm { C } = 76.67 ^ { \circ } , \mathrm { c } = 72.21 \mathrm { yd }$ $\mathrm { B } _ { 2 } = 14.75 ^ { \circ } , \mathrm { C } _ { 2 } = 120.96 ^ { \circ } , \mathrm { c } _ { 2 } = 18.89 \mathrm { yd }$

Quizplus · Accepted Answer

Given angle A and sides a and b, we can use the Law of Sines to find the possible angles B and C, and side c. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. Since the sum of angles in a triangle is 180 degrees, we can find two sets of solutions for angles B and C, leading to two different possible triangles, as indicated in option B.

Find the Missing Parts of the Triangle A=44.29∘a=51.82ydb=63.64yd\begin{array} { l } \mathrm { A } = 44.29 ^ { \circ } \\\mathrm { a } = 51.82 \mathrm { yd } \\\mathrm { b } = 63.64 \mathrm { yd }\end{array}A=44.29∘a=51.82ydb=63.64yd​

Find the Missing Parts of the Triangle $\begin{array} { l } \mathrm { A } = 44.29 ^ { \circ } \\\mathrm { a } = 51.82 \mathrm { yd } \\\mathrm { b } = 63.64 \mathrm { yd }\end{array}$