Answer:
Option C. 56 cm
Step-by-step explanation:
From the diagram attached, in ΔABC
By Pythagoras Theorem,
AB² = AC² + BC²
= 16² + 30²
= 256 +900
AB² = 1156
AB = 34
Now sinA = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{30}{34}[/tex]
A = sin⁻¹ [tex](\frac{30}{34})[/tex] = 61.93°
From ΔABD
∠A + ∠B + ∠D = 180°
61.93° + 90° + ∠D = 180°
∠D = 180 - 151.93° = 28.07°
Now tan 28.07° =[tex]\frac{BC}{CD}[/tex] = [tex]\frac{30}{CD}[/tex]
0.53328=[tex]\frac{30}{CD}[/tex]
CD = [tex]\frac{30}{0.53328}[/tex] = 56.25 cm ≈ 56 cm
Option C. 56 cm is the answer.
