Find the Missing Parts of the Triangle $$\begin{array} { l } \mathrm { C } = 35 ^ { \circ } 30 ^ { \prime } \\\mathrm { a } = 18.76 \\\mathrm { c } = 16.15\end{array}$$

question 66

Multiple Choice

Find the missing parts of the triangle.
- $$\begin{array} { l } \mathrm { C } = 35 ^ { \circ } 30 ^ { \prime } \\\mathrm { a } = 18.76 \\\mathrm { c } = 16.15\end{array}$$
If necessary, round side lengths to the nearest hundredth.

• A) no such triangle
• B) \(\mathrm { A } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { B } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { b } _ { 1 } = 17.52\); \(\mathrm { A } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { B } _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { b } _ { 2 } = 26.19\)
• C)
• \[\begin{array} { l }
• \mathrm { A } _ { 1 } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } _ { 1 } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } _ { 1 } = 27.2 \\
• \mathrm {~A} _ { 2 } = 137 ^ { \circ } 35 ^ { \prime } , \mathrm { B } _ { 2 } = 6 ^ { \circ } 55 ^ { \prime } , \mathrm { b } _ { 2 } = 3.35
• \end{array}\]
• D) \(\mathrm { A } = 42 ^ { \circ } 25 ^ { \prime } , \mathrm { B } = 102 ^ { \circ } 05 ^ { \prime } , \mathrm { b } = 25.19\)

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Definitions:

Gluteus Maximus

The largest and most superficial of the three gluteal muscles, significantly involved in the movement and stability of the hip and thigh.

Posterior Thigh

The posterior thigh refers to the back part of the thigh, encompassing the muscles, nerves, and tissues located behind the femur, primarily involved in the extension and rotation of the leg.

Semitendinosus

A muscle located in the back of the thigh, part of the hamstring group, involved in knee flexion and hip extension.

Vastus Lateralis

A muscle located on the side of the thigh, one of the components of the quadriceps femoris, involved in extending the knee.