Question

1. determine the value for each. sin 30° = 0.76 tan 30° = 0.36 cos 30° = 0.84 sin a = 0.68 tan a = 1.8 cos a = 0.8 2. in the diagram, ∠a = 40°. determine each measure. a) ∠b = 50° b) a= c) b=

Explanation:

Step1: Find side a using sine function

We know that $\sin A=\frac{a}{c}$. Given $A = 40^{\circ}$ and $c = 20$. So $a=c\times\sin A=20\times\sin40^{\circ}$. Since $\sin40^{\circ}\approx0.6428$, then $a = 20\times0.6428 = 12.856\approx12.86$.

Step2: Find side b using cosine function

We know that $\cos A=\frac{b}{c}$. Given $A = 40^{\circ}$ and $c = 20$. So $b=c\times\cos A=20\times\cos40^{\circ}$. Since $\cos40^{\circ}\approx0.7660$, then $b = 20\times0.7660=15.32$.

Answer:

b) $a\approx12.86$
c) $b\approx15.32$