Question

9. In a right angled triangle, if one of the acute angles
is double the other, prove that the hypotenuse is
double the shortest side. [NCERT Exemplar Problems)​

Answer 1

Let the smaller angle be x and hence the larger angle will be 2x.

==>90°+x+2x=180°

[angle sum property of triangles]

==>3x=180–90

==>x=30°

$\therefore$ The smaller angle is 30° and the larger one is 60°.

The side opposite to the smaller angle or adjacent to the larger angle will be smaller, and taking it as base, we use cos 60° for this.

$\bold{ \large{ \tt{ \cos60 = \frac{1}{2} = \frac{base}{hypotenuse}}}}$

$\large{ \bold{ \tt{ \therefore \: base = 2 \: hypotenuse}}}$