Question

question 1
in the figure below, what is ab?
0.21
4.24
3.77
4.51

Explanation:

Step1: Find angle \(A\)

The sum of angles in a triangle is \(180^{\circ}\). So, \(A = 180^{\circ}-63^{\circ}-71^{\circ}=46^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states \(\frac{AB}{\sin C}=\frac{AC}{\sin B}\). Here, \(AC = 4\), \(C = 71^{\circ}\), \(B = 63^{\circ}\).
Substitute into the formula: \(AB=\frac{AC\times\sin C}{\sin B}=\frac{4\times\sin71^{\circ}}{\sin63^{\circ}}\).
We know that \(\sin71^{\circ}\approx0.946\) and \(\sin63^{\circ}\approx0.891\).
Then \(AB=\frac{4\times0.946}{0.891}=\frac{3.784}{0.891}\approx4.24\).

Answer:

4.24