In a right angle triangle, two acute angles are in the ratio 2:3. Find the angles?
The two acute angles add up to 90 degrees.
Since the ratio is 2:3, divide 90 up into (2+3) parts of 18 degrees each.
Thus, the angles are
18*2 = 36 degrees
and
18*3 = 54 degrees
To find the angles of a right triangle when given the ratio of the acute angles, we can follow these steps:
Step 1: Recall that in a right triangle, one angle is always 90 degrees (the right angle). Let's denote this angle as R.
Step 2: Let's assume the measures of the two acute angles are 2x and 3x, as they are given to be in the ratio 2:3. So, one acute angle measures 2x degrees, and the other measures 3x degrees.
Step 3: Since the sum of all angles in a triangle is always 180 degrees, we can set up an equation to find x.
2x + 3x + 90 = 180
Simplifying the equation, we have:
5x + 90 = 180
5x = 180 - 90
5x = 90
x = 90 ÷ 5
x = 18
Step 4: Now that we know the value of x, we can calculate the measures of the two acute angles.
One angle: 2x = 2 * 18 = 36 degrees
Other angle: 3x = 3 * 18 = 54 degrees
Therefore, the two acute angles in the right triangle measure 36 degrees and 54 degrees, respectively.
Convert each of the following repeating decimals to
form, where a and b are integers and :
__
a. 0.7
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C 2.37
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e 4.34