Answer to Question #94534 in Geometry for Alex

Question

I'm not sure how to answer this question:
"ABC is a right-angled triangle.
AC = 14cm
Angle C = 90°
Size of angle B : size of angle A = 3 : 2

Work out the length of AB.
Give your answer correct of 3 significant figures"

How do I solve this?

Answer 1

Let the size of angle B be $3x$ and that of angle A be $2x$

So,

$90+3x+2x=180\\5x=90\\x=18$

$Size\ of\ \angle\ A=2x=36\degree\\Size\ of \angle B=3x=54\degree$

$In\ \triangle\ ABC\\\tan(\angle B)=\frac{AC}{BC}=1.3763\\So,\\BC=\frac{AC}{1.3763}=10.172$

$AB=\sqrt{AC^2+BC^2}=17.305$