Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest
tenth of a degree.
-$$\mathrm { B } = 30.4 ^ { \circ } , \mathrm { c } = 3.4 \mathrm {~mm}$$
A) $\mathrm { a } = 2.9 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 1.7 \mathrm {~mm}$
B) $\mathrm { a } = 1.7 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.9 \mathrm {~mm}$
C) $a = 2.1 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.7 \mathrm {~mm}$
D) $\mathrm { a } = 2.9 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.1 \mathrm {~mm}$

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. 
-$$\mathrm { B } = 30.4 ^ { \circ } , \mathrm { c } = 3.4 \mathrm {~mm}$$
A) $\mathrm { a } = 2.9 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 1.7 \mathrm {~mm}$ 
B) $\mathrm { a } = 1.7 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.9 \mathrm {~mm}$ 
C) $a = 2.1 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.7 \mathrm {~mm}$ 
D) $\mathrm { a } = 2.9 \mathrm {~mm} , \mathrm {~A} = 59.6 ^ { \circ } , \mathrm { b } = 2.1 \mathrm {~mm}$

Quizplus · Accepted Answer

Explanation:Using the Law of Sines, we have:$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$Substituting the given values, we get:$\frac{a}{\sin A} = \frac{1.7}{\sin 30.4^\circ} = \frac{3.4}{\sin 90^\circ}$Solving for a, we get:$a = 2.9 \mathrm{~mm}$Similarly, we can solve for A and b:$\sin A = \frac{a}{c} \sin C = \frac{2.9}{3.4} \sin 90^\circ = 0.853$$A = 59.6^\circ$$\frac{b}{\sin B} = \frac{c}{\sin C} = \frac{3.4}{\sin 90^\circ} = 3.4$$b = 1.7 \mathrm{~mm}$Therefore, the correct choice is A: $a = 2.9 \mathrm{~mm}, A = 59.6^\circ, b = 1.7 \mathrm{~mm}$.

Solve the Right Triangle Shown in the Figure B=30.4∘,c=3.4 mm\mathrm { B } = 30.4 ^ { \circ } , \mathrm { c } = 3.4 \mathrm {~mm}B=30.4∘,c=3.4 mm

Solve the Right Triangle Shown in the Figure $\mathrm { B } = 30.4 ^ { \circ } , \mathrm { c } = 3.4 \mathrm {~mm}$