Answer:
Measure of ∠ADC = 22.62°
Step-by-step explanation:
Firstly, we have right triangle ABC with AB = 12 cm and BC = 5 cm.
'Pythagoras Theorem' states that 'The sum of squares of the length of the sides in a right triangle is equal to the square of the length of the hypotenuse'.
That is, [tex]Hypotenuse^{2}=Perpendicular^{2}+Base^{2}[/tex]
i.e. [tex]AC^{2}=12^{2}+5^{2}[/tex]
i.e. [tex]AC^{2}=144+25[/tex]
i.e. [tex]AC^{2}=169[/tex]
i.e. [tex]AC=\pm 13[/tex]
As, the length of the hypotenuse cannot be negative.
So, we get, AC = 13 cm.
Further, we have a right triangle ACD with perpendicular = AC = 13 cm and hypotenuse = AD = 33.8 cm.
As we know, 'In a right angled triangle, the angles and sides can be written in trigonometric forms'.
That is, [tex]\sin ADC=\frac{perpendicular}{hypotenuse}[/tex]
i.e. [tex]\sin ADC=\frac{13}{33.8}[/tex]
i.e. [tex]\sin ADC=0.3846[/tex]
i.e. [tex]ADC=\arcsin 0.3846[/tex]
i.e. [tex]ADC=22.62[/tex]
Thus, the measure of ∠ADC = 22.62°
