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Let's go through the problems in the image you've uploaded.

### **Question 7**
In this question, you need to find the value of \( y \) using the sine ratio, given the triangle.

The triangle provided has an angle of \( 34^\circ \) and the hypotenuse is \( 10 \) units. We use the sine function:

\[
\sin 34^\circ = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{y}{10}
\]

To find \( y \):

\[
y = 10 \times \sin 34^\circ
\]

Using a calculator:

\[
\sin 34^\circ \approx 0.5592
\]

So,

\[
y = 10 \times 0.5592 = 5.592
\]

### **Question 8**
In this question, you need to calculate the value of \( y \) using the cosine ratio, given the triangle.

The triangle provided has an angle of \( 28^\circ \), the hypotenuse is \( 17 \) units, and you need to find the adjacent side \( y \):

\[
\cos 28^\circ = \frac{y}{17}
\]

To find \( y \):

\[
y = 17 \times \cos 28^\circ
\]

Using a calculator:

\[
\cos 28^\circ \approx 0.8829
\]

So,

\[
y = 17 \times 0.8829 \approx 15.009
\]

### **Question 9**
In this question, you need to use the tangent ratio to calculate the length of \( PQ \), the side opposite the angle \( 64^\circ \).

The triangle provided has an angle of \( 64^\circ \) and the adjacent side \( QR = 5 \) units. We use the tangent function:

\[
\tan 64^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{PQ}{5}
\]

To find \( PQ \):

\[
PQ = 5 \times \tan 64^\circ
\]

Using a calculator:

\[
\tan 64^\circ \approx 2.0503
\]

So,

\[
PQ = 5 \times 2.0503 \approx 10.252
\]

### **Answers:**
1. **Question 7**: \( y \approx 5.592 \)
2. **Question 8**: \( y \approx 15.009 \)
3. **Question 9**: \( PQ \approx 10.252 \)

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

Here are five related questions you might explore:

1. How can you find the angle if the lengths of two sides of a right triangle are given?
2. What is the difference between the sine, cosine, and tangent functions?
3. How do you solve a right triangle when all angles are known?
4. What are the applications of trigonometry in navigation and astronomy?
5. How do trigonometric functions change as angles increase from 0° to 90°?

**Tip:** Always check your calculator's mode (degree or radian) when solving trigonometric problems to ensure accurate results.

Learn how to solve trigonometry problems involving sine, cosine, and tangent ratios with detailed step-by-step solutions. Covering specific examples such as finding unknown sides in right triangles using trigonometric functions. Suitable for high school students.

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