Question

If the difference of the two acute angles of a right angled triangle is 2pie/5 radians, then find the angles in degrees​

Answer 1

Answer:

The angle in degrees

$= \frac{2\pi}{5} \times \frac{180}{\pi} \\ = 2 \times 36 \\ = 72$

Answer 2

Given that $\text { the difference between the two acute angles of a right-angled triangle is }$ $\frac{2\pi }{5}$

$\text { As we know that } \pi \text { гad }=180^{\circ} \Rightarrow 1 \text { гad }=180^{\circ} / \pi$ rad = 180° = 1 rad.

It is also given

hence $\begin{array}{l}2 \pi / 5 \\(2 \pi / 5 \times 180 / \pi)^{\circ}\end{array}$

$\text { By substituting the value of } \pi=22 / 7$

$\begin{array}{l}(2 \times 22 /(7 \times 5) \times 180 / 22 \times 7) \\(2 / 5 \times 180)^{\circ} \\72^{\circ}\end{array}$

$\text { Suppose one acute angle be } x^{\circ} \text { and the other acute angle be } 90^{\circ}-x^{\circ} \text {. }$

$\begin{array}{l}x^{\circ}-\left(90^{\circ}-x^{\circ}\right)=72^{\circ} \\2 x^{\circ}-90^{\circ}=72^{\circ} \\2 x^{\circ}=72^{\circ}+90^{\circ} \\2 x^{\circ}=162^{\circ} \\x^{\circ}=162^{\circ} / 2 \\x^{\circ}=81^{\circ} \text { and } \\90^{\circ}-x^{\circ}=90^{\circ}-81^{\circ} \\=9^{\circ}\end{array}$

$\text { Thus, the angles are } 81^{\circ} \text { and } 9^{\circ}$