First slide

Properties of triangles

Question

In a $△ A B C, a = 2 b$ and $A = 3 B,$ then $A =$

Moderate

A

90°
B

60°
C

30°
D

45°

Solution

We have,
$\begin{array}{l} a = 2 b \\ \Rightarrow 2 R \sin A = 4 R \sin B \\ \Rightarrow \sin A = 2 \sin B \\ \Rightarrow \sin 3 B = 2 \sin B [∵ A = 3 B] \\ \Rightarrow 3 \sin B - 4 \sin^{3} B = 2 \sin B \\ \Rightarrow \sin B - 4 \sin^{3} B = 0 \\ \Rightarrow 1 - 4 \sin^{2} B = 0 \Rightarrow \sin B = \frac{1}{2} \Rightarrow B = \frac{π}{6} \\ ∴ A = 3 B = \frac{π}{2} \end{array}$

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