Question

in a right angled triangle the acute angles are in the ratio 4:5 find the angle of the triangle in degree and radian

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Answer 1

Answer:

The angles are 40 degree and 50 degree

Step-by-step explanation:

4x+5x = 90 degree

9x = 90

x = 90/9

x = 10 degree

4x = 4(10) = 40 degree

5x = 5(10) = 50 degree

Answer 2

Step-by-step explanation:

Given:-

in a right angled triangle the acute angles are in the ratio 4:5 .

To find:-

find the angle of the triangle in degree and in radians?

Solution:-

Given triangle is a right angled triangle.

One angle must be 90°

The other angles are acute angles

The ratio of the acute angles = 4:5

Let they be =4x and 5x

We know that

the sum of all angles in a triangle is 180°

=>90°+4x+5x = 180°

=>90°+9x=180°

=>9x=180°-90°

=>9x=90°

=>x=90°/9

=>x=10°

4x=4(10°)=40°

5x=5(10°)=50°

we know that 180°=π radians

=>1°=π/180°

now, 40°=40×(π/180)

=>40°=40π/180

=>40°=2π/45 radians

and

50°=50(π/180)

=>50°=50π/180

=>50°=5π/18 radians

Answer:-

The acute angles of the given right triangle are 40° and 50°

(or)

2π/45 radians and 5π/18 radians

Used formula:-

• If one angle is 90° the triangle is a right angled triangle.
• The sum of all angles in a triangle is equal to 180°
• 180°=π radians
• 1°=π/180 radians