If there are five angles in total, three of them are cute one of them is up to us and one of them is 90°. What is the chance that two angles picked and one of them is obtuse

We are given five angles in total. Here's the breakdown of the angles based on the information provided:

1. **Three angles are acute** (less than 90°).
2. **One angle is obtuse** (greater than 90° but less than 180°). This angle is "up to us," meaning it's obtuse based on your description.
3. **One angle is 90°** (a right angle).

We are tasked with finding the probability that when two angles are randomly picked, one of them is obtuse.

### Step 1: Total number of ways to pick two angles
Since there are 5 angles in total, the number of ways to pick 2 angles is given by the combination formula:

\[
\text{Total combinations} = \binom{5}{2} = \frac{5 \times 4}{2} = 10
\]

### Step 2: Favorable outcomes (one obtuse angle and one non-obtuse)
To satisfy the condition of selecting one obtuse angle, we need to:
- Choose the one obtuse angle (which is just 1).
- Pair it with any of the other angles (4 remaining angles, which are either acute or 90°).

The number of favorable outcomes is simply 1 (the obtuse angle) multiplied by the 4 remaining angles to choose from:

\[
\text{Favorable outcomes} = 1 \times 4 = 4
\]

### Step 3: Probability calculation
The probability is the ratio of favorable outcomes to the total possible combinations of choosing two angles:

\[
P(\text{one obtuse angle}) = \frac{4}{10} = 0.4
\]

Thus, the probability that one of the two randomly chosen angles is obtuse is **0.4**, or **40%**.

---

Would you like further details or clarification on any part of this explanation?

Here are 5 related questions to think about:
1. How do you calculate the probability of selecting two acute angles instead?
2. What would change if there were two obtuse angles instead of one?
3. How would the result change if there were no 90° angle?
4. How is the combination formula \(\binom{n}{r}\) derived, and how does it apply to this situation?
5. What if we were selecting three angles instead of two?

**Tip:** For problems involving probability, always check whether the events you're considering are independent or dependent!

If there are five angles in total, three of them are cute one of them is up to us and one of them is 90°. What is the chance that two angles picked and one of them is obtuse?

Learn how to calculate the probability of picking an obtuse angle from a set of five angles, including three acute, one obtuse, and one right angle. This problem explores basic probability concepts and uses combinatorics to determine the solution. Suitable for students in Grades 6-8.

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