Find the missing parts of the triangle.
-A = 10.5° a = 149 ft
B = 176 ft
If necessary, round angles to the nearest tenth and side lengths to the nearest foot.
A) no such triangle
B) $\mathrm { B } _ { 1 } = 157.1 ^ { \circ } , \mathrm { C } _ { 1 } = 12.4 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }$
$\mathrm { B } _ { 2 } = 1.9 ^ { \circ } , \mathrm { C } _ { 2 } = 167.6 ^ { \circ } , \mathrm { c } _ { 2 } = 27 \mathrm { ft }$
C) $\mathrm { B } = 12.4 ^ { \circ } , \mathrm { C } = 157.1 ^ { \circ } , \mathrm { c } = 318 \mathrm { ft }$
D) $\mathrm { B } _ { 1 } = 12.4 ^ { \circ } , \mathrm { C } _ { 1 } = 157.1 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }$
$\mathrm { B } _ { 2 } = 167.6 ^ { \circ } , \mathrm { C } _ { 2 } = 1.9 ^ { \circ } , \mathrm { c } _ { 2 } = 27 \mathrm { ft }$

Question

Find the missing parts of the triangle.
-A = 10.5° a = 149 ft
B = 176 ft
If necessary, round angles to the nearest tenth and side lengths to the nearest foot. 
A) no such triangle
B) $\mathrm { B } _ { 1 } = 157.1 ^ { \circ } , \mathrm { C } _ { 1 } = 12.4 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }$
$\mathrm { B } _ { 2 } = 1.9 ^ { \circ } , \mathrm { C } _ { 2 } = 167.6 ^ { \circ } , \mathrm { c } _ { 2 } = 27 \mathrm { ft }$
C) $\mathrm { B } = 12.4 ^ { \circ } , \mathrm { C } = 157.1 ^ { \circ } , \mathrm { c } = 318 \mathrm { ft }$
D) $\mathrm { B } _ { 1 } = 12.4 ^ { \circ } , \mathrm { C } _ { 1 } = 157.1 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }$
$\mathrm { B } _ { 2 } = 167.6 ^ { \circ } , \mathrm { C } _ { 2 } = 1.9 ^ { \circ } , \mathrm { c } _ { 2 } = 27 \mathrm { ft }$

Quizplus · Accepted Answer

Given the sides a and B, we can use the Law of Sines to find the missing angles and side. The sum of angles in a triangle is 180°, so we can calculate the other angles and use the Law of Sines again to find the missing side. The options with two possible triangles (B1, C1, c1 and B2, C2, c2) reflect the fact that there can be two different triangles (ambiguous case) depending on the angle's sine value.

Find the Missing Parts of the Triangle B1=157.1∘,C1=12.4∘,c1=318ft\mathrm { B } _ { 1 } = 157.1 ^ { \circ } , \mathrm { C } _ { 1 } = 12.4 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }B1​=157.1∘,C1​=12.4∘,c1=318ft

Find the Missing Parts of the Triangle $\mathrm { B } _ { 1 } = 157.1 ^ { \circ } , \mathrm { C } _ { 1 } = 12.4 ^ { \circ } , \mathrm { c } 1 = 318 \mathrm { ft }$