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.