Question

10 fill in the blank 1 point let abc be a triangle such that angle a is opposite side a, angle b is opposite side b, and angle c is opposite side c. if ( b = 120.87^{circ}, a = 15 ), and ( b = 20 ), solve for angle a. round your answer to the nearest hundredth of a degree. ( mangle a=) type your answer_ 11 hot spot 1 point select the quadrant the terminal side of the following angle is in. ( -271^{circ} )

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). We know \(a = 15\), \(b = 20\), and \(B=120.87^{\circ}\). So, \(\sin A=\frac{a\sin B}{b}\).

Step2: Substitute the values

Substitute \(a = 15\), \(b = 20\), and \(B = 120.87^{\circ}\) into the formula. \(\sin A=\frac{15\times\sin(120.87^{\circ})}{20}\). First, calculate \(\sin(120.87^{\circ})\approx0.859\). Then \(\sin A=\frac{15\times0.859}{20}=\frac{12.885}{20}=0.64425\).

Step3: Find angle \(A\)

Since \(A=\sin^{- 1}(0.64425)\), using a calculator, \(A\approx40.17^{\circ}\).

Answer:

\(40.17\)