The diagram illustrates a right-angled triangle where we need to find the height $p$ of the house. Here's the given information:

• The horizontal distance between the wall and the house is 5.47 m.
• The vertical height of the wall is 2.64 m.
• The angle between the bunting and the horizontal line is $36^\circ$.

We can use trigonometry to solve this problem.

Step-by-Step Process:

1. The total height of the right triangle is the sum of the height of the wall (2.64 m) and the unknown height of the house $p$.

   Let the total height be denoted as $H = p + 2.64$.

2. We can use the tangent function in trigonometry. Tangent is defined as: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ In this case:

   • $\theta = 36^\circ$
   • Opposite side = $H$ (the total height)
   • Adjacent side = 5.47 m

   So the equation becomes: $\tan(36^\circ) = \frac{H}{5.47}$

3. Solving for $H$: $H = 5.47 \times \tan(36^\circ)$

4. Once we find $H$, subtract the height of the wall (2.64 m) to get $p$.

Now, I will calculate the values.The height $p$ of the house is approximately 1.33 meters, rounded to two decimal places.

Would you like further details or have any additional questions?

Here are 5 related questions to expand on this topic:

1. How would the height of the house change if the angle was increased to 45°?
2. What if the horizontal distance was reduced to 4 meters, how would that affect $p$?
3. Can you explain why we used the tangent function and not sine or cosine in this case?
4. How would we calculate the length of the bunting line between the wall and the house?
5. How could you solve this problem without using trigonometry, if possible?

Tip: When solving triangle problems involving angles, make sure you understand which trigonometric function (sine, cosine, tangent) corresponds to the sides you're working with.