Question

1. a) determine length b to the nearest tenth of a centimetre.

a
b?
27.2 cm
43°
c
72°
b
ngle trigonometry

Explanation:

Step1: Find angle A

The sum of angles in a triangle is 180°. So, $A=180^{\circ}-72^{\circ}-43^{\circ}=65^{\circ}$.

Step2: Apply the sine - law

The sine - law states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we know side $c = 27.2$ cm, $C = 43^{\circ}$, and $B=72^{\circ}$. Using $\frac{b}{\sin B}=\frac{c}{\sin C}$, we can solve for $b$. So, $b=\frac{c\sin B}{\sin C}$.

Step3: Substitute the values

Substitute $c = 27.2$, $\sin B=\sin72^{\circ}\approx0.9511$, and $\sin C=\sin43^{\circ}\approx0.6820$ into the formula. $b=\frac{27.2\times0.9511}{0.6820}$.

Step4: Calculate the value of b

$b=\frac{27.2\times0.9511}{0.6820}=\frac{25.86992}{0.6820}\approx37.9$ cm.

Answer:

$37.9$ cm