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### **Question 5**
You are given a right-angled isosceles triangle with the right angle at \( A \). You need to find the value of \( \tan B \) in this triangle.

For a right-angled isosceles triangle:
- The two legs (sides opposite the angles \( A \) and \( B \)) are equal.
- The angles opposite these sides are equal, each being \( 45^\circ \) because the sum of the angles in a triangle is \( 180^\circ \).

Since \( \tan B \) is the ratio of the opposite side to the adjacent side in a right triangle:

\[
\tan B = \frac{\text{opposite side to } B}{\text{adjacent side to } B} = \frac{\text{leg}}{\text{leg}} = 1
\]

### **Question 6**
You need to calculate \( 6 \times \tan 35^\circ \) to three decimal places.

Using a calculator:

\[
\tan 35^\circ \approx 0.7002
\]

So,

\[
6 \times 0.7002 = 4.2012
\]

Rounding to three decimal places:

\[
6 \times \tan 35^\circ \approx 4.201
\]

### **Answers:**
1. **Question 5**: \( \tan B = 1 \)
2. **Question 6**: \( 6 \times \tan 35^\circ \approx 4.201 \)

Would you like more details on these solutions or have any questions?

Here are five related questions you might explore:

1. How do you calculate \( \sin B \) in a right-angled isosceles triangle?
2. What are the properties of an isosceles triangle?
3. How does \( \tan 45^\circ \) compare to \( \tan 30^\circ \) and \( \tan 60^\circ \)?
4. What are the applications of trigonometric ratios in real-world problems?
5. How do you convert degrees to radians in trigonometry?

**Tip:** Remember, for any right-angled isosceles triangle, the angles other than the right angle are always \( 45^\circ \).

Explore how to solve trigonometric problems involving right-angled isosceles triangles. This page provides detailed solutions to questions on finding \( \tan B \) and calculating expressions using trigonometric ratios. Suitable for high school students studying trigonometry.

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