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

Step-by-step explanation:

The sum of the acute angles of a right-angled triangle is 90°

Let angles be 4x and 5x.

+ 4x+5x=90°

9x=90

x=10

So, angles are:

4x=40°

5x=50°

rad(40%) = 21/9 [Multiply by /180°)

rad(50%) = 51/18

Answer 2

Given,

In a right-angled triangle, the ratio of the acute angles = 4:5

To find,

The acute angles of the triangle in degree and radian.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

Sum of all the angles of any triangle = 180°

Also, radians = degrees × π/180

Now, according to the question;

Let us assume that both acute angles of the right-angled triangle are 5x and 4x, respectively.

Now,

Sum of all the angles of the given right-angled triangle = 180°

=> 90° + 5x + 4x = 180°

=> 9x = 90°

=> x = 10°

So, the first acute angle of the given right-angled triangle = 5x = 5 x 10° = 50° (in degrees)

= (5π/18) radians

And,

the second acute angle of the given right-angled triangle = 4x = 4 x 10° = 40° (in degrees)

= (2π/9) radians

Hence, both acute angles of the given right-angled triangle are 50°, 40° in degrees and (5π/18) radians, (2π/9) radians in radians.