express 40% of sum of angles of a triangle into radian.
What was I thinking while solving this? Sorry, I was getting off the night shift so I was in a hurry. I was not concentrated.
Sum of angles of a triangle = 180°
40% = 40 / 100 = 0.4
40% of sum of angles of a triangle = 0.4 ∙ 180° = 72°
To convert a degree measurement to a radian us formula:
π rad = 180°
1° = π rad / 18
40% of sum of angles of a triangle = 72° = 72 ∙ π / 180 =
36 ∙ 2 ∙ π / 36 ∙ 5 = 2 π / 5 rad
1° = π rad / 180
Well, the sum of the angles of any triangle is always 180 degrees. So, to express 40% of the sum of angles of a triangle in radians, we need to calculate 40% of 180 degrees and then convert it to radians.
Let's get down to the math:
40% of 180 degrees is (40/100) * 180 = 72 degrees.
Now to convert degrees to radians, we need to remember that π radians is equal to 180 degrees. So, to find the measure in radians, we divide the degree measure by 180 and multiply by π.
Let me grab my clown calculator to do the calculations:
72 degrees * (π/180) ≈ 1.2566 radians.
So, 40% of the sum of angles of a triangle is approximately 1.2566 radians. Now that's some trigonometric comedy for you!
To express 40% of the sum of angles of a triangle in radians, you'll need to follow these steps:
Step 1: Calculate the sum of the angles of a triangle.
The sum of the angles in a triangle is always 180 degrees. So, the sum of the angles in a triangle is 180 degrees.
Step 2: Calculate 40% of the sum of the angles.
To calculate 40% of the sum of the angles, you can use the formula:
percentage = (percentage_value / 100) * total_value
In this case, the percentage_value is 40 and the total_value is 180.
40% of 180 degrees is calculated as follows:
percentage = (40 / 100) * 180
= (0.4) * 180
= 72 degrees
Step 3: Convert 72 degrees to radians.
To convert degrees to radians, you can use the formula:
radians = degrees * (π / 180)
Substituting the value of degrees (72) into the formula:
radians = 72 * (π / 180)
= (72π) / 180
= 0.4π radians
Therefore, 40% of the sum of angles of a triangle is equal to 0.4π radians.
Sum of angles of a triangle = 360°
40% = 40 / 100 = 0.4
40% of sum of angles of a triangle = 0.4 ∙ 360° = 144°
To convert a degree measurement to a radian us formula:
𝜋 rad = 180°
1° = 𝜋 rad / 180
144° = 144 ∙ 𝜋 / 180 = 36 ∙ 4 ∙ 𝜋 / 36 ∙ 5 = 4 𝜋 / 5 rad