Question

By first calculating the size of angle LMN, calculate the area of triangle MNL. You must show all your working.

Answer 1

Answer:

m(∠LMN) = 67.44°

Area of ΔMNL = 16.66 square units

Step-by-step explanation:

By applying Sine rule in the ΔLMN,

$\frac{\text{Sin}M}{\text{NL}}=\frac{\text{Sin}N}{\text{ML}}$

$\frac{\text{Sin}M}{7.2}}=\frac{\text{Sin}38}{\text{4.8}}$

SinM = $\frac{\text{Sin}38\times 7.2}{4.8}$

SinM = 0.9235

M = $\text{Sin^{-1}}(0.9235)$$\text{Sin}^{-1} (0.9235)$

M = 67.44°

m(∠M) + m(∠N) + m(∠L) = 180°

67.44 + 38 + m(∠L) = 180°

m(∠L) = 180 - 105.44

m(∠L) = 74.56°

Area of ΔMNL = $\frac{1}{2}(\text{ML})(\text{NL})\text{Sin}(74.56)$

                        = $\frac{1}{2}(4.8)(7.2)(0.96391)$

                        = 16.66 square units