The difference between the two acute angles of a right angled triangle is 2pie /5 radians . Express the angle of the triangle in degree and grade .
well, the two angles add to pi/2, so if x is the smaller angle,
x + (x+2pi/5) = pi/2
2x = pi/10
x = pi/20
So, the two angles are pi/20 and 9pi/20
A wheel makes 180 revolutions in 1 minute , through how many radians does it turns in 1 seconds
180rev/1min * 1min/60s * 2π rad/rev = 6π rad/s
To find the angles of a right-angled triangle when given the difference between the acute angles, we'll first solve for one of the acute angles and then calculate the other angle.
1. Let's denote the two acute angles of the right-angled triangle as A and B. We are given that the difference between these angles is 2π/5 radians.
2. Since the sum of the interior angles of a triangle is always 180 degrees or π radians, we know that A + B + 90 degrees (or π/2 radians) = 180 degrees (or π radians).
3. Rearranging the equation, we find A + B = 180 degrees (or π radians) - 90 degrees (or π/2 radians) = 90 degrees (or π/2 radians).
4. We are also given that the difference between the angles is 2π/5 radians. So we can write A - B = 2π/5 radians.
5. Now, we have a system of two equations:
A + B = 90 degrees (or π/2 radians) (Equation 1)
A - B = 2π/5 radians (Equation 2)
6. To solve this system of equations, we can add Equation 1 and Equation 2, resulting in 2A = 90 degrees (or π/2 radians) + 2π/5 radians.
7. Simplifying the equation, we get 2A = (5π + 4π) / 10 = 9π/10.
8. Dividing both sides by 2, we find A = 9π/20 radians.
9. To convert radians to degrees, we multiply by 180/π. So, A = (9π/20 radians) * (180/π) = 162 degrees.
10. Since A is an acute angle, B = 90 degrees - A = 90 degrees - 162 degrees = -72 degrees. However, angles cannot be negative, so B = 360 degrees - 72 degrees = 288 degrees.
11. To convert the angles to grades, we multiply by 10/9. So, A in grades = (162 degrees) * (10/9) = 180 grades and B in grades = (288 degrees) * (10/9) = 320 grades.
Therefore, the acute angles of the right-angled triangle are approximately 162 degrees and 288 degrees, or 180 grades and 320 grades, respectively.