the acute angles of a right triangle are in the ratio 2 is to 3 find the angles of the triangle
Answers
Let the measure of the two angles be 2x and 3x (Since 2:3)
2x + 3x + 90° = 180°
5x = 180° - 90°
5x = 90
x = 90/5
x = 18
Therefore, one angle is 2x = 2*18 = 36°, second angle is 3x = 3*18 = 54° and the third one is 90° as it is a right angled triangle.
Hope it helps :)
Given - Ratio of acute angles
Find - Angles
Solution - Let the acute angles be 2x and 3x. As per the known fact, sum of angles of triangle is 180° and one angle of right angled triangle is 90°. Representing this in mathematical expression -
2x + 3x + 90 = 180
Performing addition
5x + 90 = 180
Shifting 90 to Right Hand Side and performing subtraction
5x = 180 - 90
5x = 90
Shifting 5 to Right Hand Side and performing division
x = 90/5
x = 18°
Acute angle = 2x and 3x
Acute angle = 2*18 and 3*18
Performing multiplication
Acute angle = 36° and 54°
Hence, the angles of triangle are 90°, 36° and 54°.