In A Right Angled Triangle,one Of The Acute Angles Is 20degree Greater Than The Other. Find The Angles Of The Triangle.
smaller angle --- x
larger angle --- x+20
x + x+20 + 90 = 180
2x = 70
x = 35
the angles are 35° , 55° and 90°
Construct a right angled triangle having hypotenuse of length 5.6 cm and with one of the acute angles 30
Show working
To find the angles of a right-angled triangle, we can use the fact that the sum of all angles in a triangle is equal to 180 degrees.
Let's suppose that one of the acute angles is represented by x degrees. According to the problem, the other acute angle is 20 degrees greater than x, so it can be represented by (x + 20) degrees.
Since the sum of all angles in a triangle is equal to 180 degrees, we can write the equation as:
x + (x + 20) + 90 = 180
Simplifying this equation, we get:
2x + 110 = 180
Subtracting 110 from both sides, we have:
2x = 70
Dividing both sides by 2, we find:
x = 35
Therefore, one of the acute angles is 35 degrees, and the other acute angle is (35 + 20) = 55 degrees.
The right angle in the triangle is always 90 degrees.
So, the angles of the triangle are:
Right Angle: 90 degrees
Acute Angle 1: 35 degrees
Acute Angle 2: 55 degrees