3. In a right-angled triangle, two acute angles are in a ratio of 2 : 3. Find the measures of the angles
Answers
Step-by-step explanation:
Given:-
In a right-angled triangle, two acute angles are in a ratio of 2 : 3.
To find:-
Find the measures of the angles?
Solution:-
Method-1:-
The ratio of two acute angles in a right angled triangle = 2:3
Let the two acute angles be 2X° and 3X°
Since it is the right angled triangle one angle must be 90°
We know that
The sum of all the three angels in a triangle is 180°
=>90° +2X° +3X° = 180°
=>5X° +90° = 180°
=>5X° = 180° - 90°
=>5X° = 90°
=>X ° = 90°/5
=>X° = 18°
The value of X° = 18°
2X° = 2×18° = 36°
3X° = 3×18° = 54°
The two acute angles are 36° and 54°
Method-2:-
The ratio of two acute angles in a right angled triangle = 2:3
Let the two acute angles be 2X° and 3X°
Since it is the right angled triangle one angle must be 90°
The two acute angles are complementary angles
We know that
The sum of two angles is 90° they are complementary angles
=>2X° + 3X° = 90°
=>5X° = 90°
=>X ° = 90°/5
=>X° = 18°
The value of X° = 18°
2X° = 2×18° = 36°
3X° = 3×18° = 54°
The two acute angles are 36° and 54°
Answer:-
The two acute angles of the given right angled triangle are 36° and 54°.
Used formulae:-
- If one angle is 90° then the triangle is a right angled triangle.
- The sum of all the three angels in a triangle is 180°
- The sum of two angles is 90° they are complementary angles.