Certainly! Let's solve the given problem step-by-step.
### Step-by-Step Solution
#### Given:
We have a right-angled triangle and one of the acute angles is 60°.
#### To Find:
1. The other acute angle in degrees.
2. The other acute angle in radians.
#### Solution:
1. Finding the other acute angle in degrees:
In a right-angled triangle, the sum of the two acute angles is always 90°. This is because the right angle itself is 90°, and the sum of all angles in a triangle is always 180°.
Given one acute angle is 60°, we can find the other acute angle by subtracting this from 90°:
[tex]\[
\text{Other acute angle} = 90° - 60° = 30°
\][/tex]
So, the other acute angle is 30°.
2. Converting the angles to radians:
The formula to convert degrees to radians is:
[tex]\[
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
\][/tex]
- Converting 60° to radians:
[tex]\[
60° \times \frac{\pi}{180} = \frac{60 \pi}{180} = \frac{\pi}{3} \approx 1.0471975511965976 \text{ radians}
\][/tex]
- Converting 30° to radians:
[tex]\[
30° \times \frac{\pi}{180} = \frac{30 \pi}{180} = \frac{\pi}{6} \approx 0.5235987755982988 \text{ radians}
\][/tex]
So, the other acute angle in a right-angled triangle where one of the acute angles is 60° is:
(a) In degrees: 30°
(b) In radians: [tex]\(\approx 0.5235987755982988\)[/tex] radians
