Question

solve the following triangle.
a = 70°, b = 10°, a = 7
c ≈ □°
(simplify your answer.)
b ≈ □
(type an integer or decimal rounded to two decimal places as n
c ≈ □
(type an integer or decimal rounded to two decimal places as n

Explanation:

Step1: Find angle \( C \)

The sum of angles in a triangle is \( 180^{\circ} \). So \( C=180^{\circ}-A - B \).
Substitute \( A = 70^{\circ} \) and \( B = 10^{\circ} \):
\( C=180^{\circ}-70^{\circ}-10^{\circ}=100^{\circ} \)

Step2: Find side \( b \) using the Law of Sines

The Law of Sines is \( \frac{a}{\sin A}=\frac{b}{\sin B} \).
We know \( a = 7 \), \( A = 70^{\circ} \), \( B = 10^{\circ} \).
So \( b=\frac{a\sin B}{\sin A} \).
\( \sin 70^{\circ}\approx0.9397 \), \( \sin 10^{\circ}\approx0.1736 \)
\( b=\frac{7\times0.1736}{0.9397}\approx1.29 \)

Step3: Find side \( c \) using the Law of Sines

Using \( \frac{a}{\sin A}=\frac{c}{\sin C} \)
\( \sin C=\sin 100^{\circ}\approx0.9848 \)
\( c=\frac{a\sin C}{\sin A}=\frac{7\times0.9848}{0.9397}\approx7.33 \)

Answer:

\( C = 100^{\circ}\), \( b\approx1.29 \), \( c\approx7.33 \)