If one side of a triangle is double the other and the angles opposite to these sides differ by , then the triangle is
Right-angled
Explanation for the correct option.
Step 1: Information required for the solution
Let one side of the triangle be then the other side will be .
Suppose the angle opposite to the side be then the angle opposite to the side will be .
Now, the sine rule is given by when three sides are with the angles opposite to these sides are respectively
Step 2: Determination of the type of a triangle
Apply this rule for the assumed parameters,
The numerator of the RHS can be expanded by applying the trigonometric identity ,
This proves that one angle is a right angle and the two angles will be . Therefore, the triangle is right-angled.
Hence, the correct option is (D).