How to solve the following question attached?

Question

asked Jan 17, 2022 232k views

1 Answer

Annamae · Answer 1 · 2022-01-22T00:35:00+0000

Answer: AB=21.88 mm, BC=51.54 mm

Explanation:

Given

$\angle A=67^(\circ)$

$AC=56\ mm$

The other two sides can find out using trigonometry

$\Rightarrow \sin 67^(\circ)=(BC)/(AC)\\\\\Rightarrow \sin 67^(\circ)=(BC)/(56)\\\\\Rightarrow BC=56\sin 67^(\circ)\\\Rightarrow BC=51.54\ mm$

Similarly, for AB

$\Rightarrow \cos 67^(\circ)=(AB)/(AC)\\\\\Rightarrow \cos 67^(\circ)=(AB)/(56)\\\\\Rightarrow AB=56\cos 67^(\circ)\\\Rightarrow AB=21.88\ mm$

Angle C is given by

$\angle C=90^(\circ)-67^(\circ)\\\angle C=23^(\circ)$