Question

How to solve the following question attached?

Answer 1

Answer: AB=21.88 mm, BC=51.54 mm

Step-by-step explanation:

Given

$\angle A=67^{\circ}$

$AC=56\ mm$

The other two sides can find out using trigonometry

$\Rightarrow \sin 67^{\circ}=\dfrac{BC}{AC}\\\\\Rightarrow \sin 67^{\circ}=\dfrac{BC}{56}\\\\\Rightarrow BC=56\sin 67^{\circ}\\\Rightarrow BC=51.54\ mm$

Similarly, for AB

$\Rightarrow \cos 67^{\circ}=\dfrac{AB}{AC}\\\\\Rightarrow \cos 67^{\circ}=\dfrac{AB}{56}\\\\\Rightarrow AB=56\cos 67^{\circ}\\\Rightarrow AB=21.88\ mm$

Angle C is given by

$\angle C=90^{\circ}-67^{\circ}\\\angle C=23^{\circ}$