Question

solving a triangle given sas information
using the law of cosines, ( a approx ),
rounded to the nearest tenth.
complete
use your answer above to find ( m angle b ). to the
nearest degree, ( m angle b approx )

Explanation:

Step1: Apply the Law of Sines

The Law of Sines is \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). We know \(a = 2.2\), \(A=33^{\circ}\), and \(b = 4.0\). From \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we can rewrite it as \(\sin B=\frac{b\sin A}{a}\).

Step2: Substitute the values

Substitute \(a = 2.2\), \(b = 4.0\), and \(A = 33^{\circ}\) into the formula. \(\sin B=\frac{4.0\times\sin(33^{\circ})}{2.2}\). First, calculate \(\sin(33^{\circ})\approx0.5446\). Then \(\frac{4.0\times0.5446}{2.2}=\frac{2.1784}{2.2}\approx0.99\).

Step3: Find the angle \(B\)

Since \(B=\sin^{- 1}(0.99)\), and \(\sin^{-1}(x)\) gives the angle whose sine is \(x\). \(B\approx82^{\circ}\) (because \(\sin(82^{\circ})\approx0.99\) and considering the range of angles in a triangle \(0^{\circ}

Answer:

\(82\)