Question

Find the length of side AB.

Answer 1

Answer:

8.86 cm

Step-by-step explanation:

The sine rule shows the relationship between the sides of a triangle and its opposite sides. Sine rule states that given a triangle with side a and opposite angle A, side b and opposite angle B, side c and opposite angle C then:

$\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}$

From the image attached, let AB = x, its opposite angle is 41°. BC = 13.5 cm and its opposite angle is 90°  (right angle). Therefore using sine rule:

$\frac{x}{sin(41)} =\frac{13.5}{sin(90)} \\\\x=sin(41)*\frac{13.5}{sin(90)}\\\\x=8.8568\\\\ x=8.86\ cm\ to\ 3\ s.f$

x = AB = 8.86 cm