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How to solve the following question attached?

How To Solve The Following Question Attached class=

Sagot :

Answer: AB=21.88 mm, BC=51.54 mm

Step-by-step explanation:

Given

[tex]\angle A=67^{\circ}[/tex]

[tex]AC=56\ mm[/tex]

The other two sides can find out using trigonometry

[tex]\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[/tex]

Similarly, for AB

[tex]\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[/tex]

Angle C is given by

[tex]\angle C=90^{\circ}-67^{\circ}\\\angle C=23^{\circ}[/tex]