Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree.
-$$b = 120 , c = 470$$
A) $\mathrm { A } = 75.2 ^ { \circ } , \mathrm { B } = 14.8 ^ { \circ } , \mathrm { a } = 454.4$
B) $\mathrm { A } = 75.2 ^ { \circ } , \mathrm { B } = 14.8 ^ { \circ } , \mathrm { a } = 485.1$
C) $\mathrm { A } = 75.7 ^ { \circ } , \mathrm { B } = 14.3 ^ { \circ } , \mathrm { a } = 485.1$
D) $\mathrm { A } = 14.3 ^ { \circ } , \mathrm { B } = 75.7 ^ { \circ } , \mathrm { a } = 454.4$

Question

Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree. 
-$$b = 120 , c = 470$$
A) $\mathrm { A } = 75.2 ^ { \circ } , \mathrm { B } = 14.8 ^ { \circ } , \mathrm { a } = 454.4$ 
B) $\mathrm { A } = 75.2 ^ { \circ } , \mathrm { B } = 14.8 ^ { \circ } , \mathrm { a } = 485.1$ 
C) $\mathrm { A } = 75.7 ^ { \circ } , \mathrm { B } = 14.3 ^ { \circ } , \mathrm { a } = 485.1$ 
D) $\mathrm { A } = 14.3 ^ { \circ } , \mathrm { B } = 75.7 ^ { \circ } , \mathrm { a } = 454.4$

Quizplus · Accepted Answer

Given $b = 120$ and $c = 470$, we can use the Law of Sines to find angle $A$ or $B$ and then use the sum of angles in a triangle to find the other angle. The Law of Sines states that $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$. Without specific calculations provided in the options, we can't directly calculate the angles or side $a$, but we can infer correctness based on the properties of triangles.Option A suggests angles that are complementary (adding up to $90^\circ$) and a side $a$ length that seems plausible given the lengths of sides $b$ and $c$. However, the angles given in Option A actually add up to $90^\circ$, which is not possible for a non-right triangle (and if it were a right triangle, the given sides do not satisfy the Pythagorean theorem). This explanation was based on a misunderstanding of the question's requirements and the provided information. Without the ability to directly calculate and verify the values based on the given sides $b$ and $c$, determining the correct option requires applying the Law of Sines or Cosines correctly, which was not done here. The correct approach involves calculating or logically deducing which set of angles and side lengths are consistent with the given side lengths and the properties of triangles, specifically using the Law of Sines to relate the sides and angles.

Solve the Right Triangle Shown in the Figure b=120,c=470b = 120 , c = 470b=120,c=470

Solve the Right Triangle Shown in the Figure $b = 120 , c = 470$