Question

In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degree and radian....​

Answer 1

$\huge\fbox{Answer ☘}$

since we've a right angled triangle

therefore , one angle of the triangle is 90°

applying Angle Sum Property of triangle which states that the sum of all the angles of a triangle is equal to 180° , we get

$4x + 5x + 90° = 180° \\\\ 9x + 90° = 180° \\\\ 9x = 180° - 90° \\\\ 9x = 90° \\\\ x = \frac{\cancel{90}}{\cancel{9}} = 10°$

therefore , the angles are

( In degree measure )

$\bold\blue{4x = 4 ( 10 ) = 40°}\\\bold\blue{5x = 5 ( 10 ) = 50°}$

( In radians )

$40 \: in \: radians = \frac{\pi}{18\cancel{0}} \times 4\cancel{0} \\ \bold\blue{ = > \frac{4\pi}{18} \: radians}$

$50 \: in \: radians = \frac{\pi}{18\cancel{0}} \times 5\cancel{0} \\ \bold\blue{= > \frac{5\pi}{18} \: radians}$

hope helpful~