The difference between the two acute angles of a right-angled triangle is 2(pie)/5 radians. Express the angles in degrees?? How to Solve it
2π/5 radians = 72°
so let one angle be x
then the other is x+72
we know x + x+72 = 90
2x = 18
x = 9
So the two angles are 9° and 81°
To solve the problem, follow these steps:
Step 1: Let's assume that one of the acute angles is x degrees.
Step 2: Since the two acute angles in a right-angled triangle add up to 90 degrees, the other acute angle can be expressed as (90 - x) degrees.
Step 3: Now, we need to convert the given difference between the angles, which is 2(pi)/5 radians, into degrees. Recall that one full revolution in radians is equal to 360 degrees. So, we can use this conversion: (2(pi)/5 radians) * (180 degrees / pi radians) = 72 degrees.
Step 4: Since the difference between the angles is 72 degrees, we can set up the equation: (90 - x) - x = 72.
Step 5: Simplify the equation: 90 - 2x = 72.
Step 6: Solve for x: 2x = 90 - 72 = 18.
Step 7: Divide both sides by 2: x = 9.
Step 8: Now, we know that one of the acute angles is 9 degrees, so the other acute angle is (90 - 9) = 81 degrees.
Therefore, the two acute angles of the right-angled triangle are 9 degrees and 81 degrees.
To solve this problem, we'll start by understanding the information given.
In a right-angled triangle, one angle is a right angle, which measures 90 degrees or π/2 radians. Let's call the other two angles A and B. According to the problem, the difference between these two acute angles is 2π/5 radians.
Now, we need to find the measures of angles A and B in degrees.
To convert radians to degrees, we use the conversion factor 180/π. So, we can express angles A and B in degrees as follows:
A = (2π/5) * (180/π) = (2/5) * 180 = 360/5 = 72 degrees
B = A + (2π/5) * (180/π) = 72 + 72 = 144 degrees
Therefore, the two acute angles of the right-angled triangle are 72 degrees and 144 degrees.
x+9+81=90
x+90=90
x=90-90
x=o