Question

part 2 of 3
solve the triangle.
a=3, b=7, c=10°

c≈ 4.1
(do not round until the final answer. then round to the nearest tenth as needed.)
a≈ □°
(do not round until the final answer. then round to the nearest degree as needed.)
help me solve this view an example get more help
review progress question 28 of 35

Explanation:

Step1: Use Law of Sines

We know \( \frac{a}{\sin A}=\frac{c}{\sin C} \). Given \( a = 3 \), \( c\approx4.1 \), \( C = 10^\circ \). So \( \sin A=\frac{a\sin C}{c} \).

Step2: Calculate \( \sin A \)

Substitute values: \( \sin A=\frac{3\sin10^\circ}{4.1} \). \( \sin10^\circ\approx0.1736 \), so \( \sin A=\frac{3\times0.1736}{4.1}\approx\frac{0.5208}{4.1}\approx0.127 \).

Step3: Find angle \( A \)

\( A=\arcsin(0.127)\approx7.3^\circ\approx7^\circ \) (rounded to nearest degree).

Answer:

\( 7 \)