if 5 tan Ais 12 then what is 13/3 sin A Please show me the working thanks - Maths - Introduction to Trigonometry

Question

if 5 tan Ais 12 then what is 13/3 sin A ? Please show me the
working thanks

Pronay · Accepted Answer

$5 \tan A = 12 \Rightarrow \tan A = \frac{12}{5} = \frac{perpendicular}{base}$

Therefore

${Hypotenuse}^{2} = {perpendicular}^{2} + {base}^{2} = 12^{2} + 5^{2} = 144 + 25 = 169 hypotenuse= \sqrt{169} = 13$

$\Rightarrow \sin A = \frac{perpendicular}{hypotenuse} = \frac{12}{13}$

Therefore

$\frac{13}{3} \sin A = \frac{13}{3} \times \frac{12}{13} = 4$

if 5 tan Ais 12 then what is 13/3 sin A ? Please show me the working. thanks.