If a simple hip roof is used with an angle of 25°, what will be the length of the longest span of the roofing sheet?

Steps to Solve

1. Identify the Triangle Dimensions

   For a hip roof, we can visualize a right triangle where the length of the span is the hypotenuse. If we denote the length of the span as ( L ) and the angle of the roof as ( \theta = 25^\circ ), we can use trigonometric functions to relate the angle to the lengths.

2. Apply Trigonometric Functions

   The length of the span relates to the height and base of the triangle. Using the sine function:

   $$ \sin(\theta) = \frac{\text{opposite}}{L} $$

   For the longest span of the roofing sheet, set the opposite side to the height of the roof; without loss of generality, let's assume we need to find ( L ) alone, thus rearranging gives:

   $$ L = \frac{\text{height}}{\sin(25^\circ)} $$

3. Determine the Required Height

   Without a specified height in the problem, we can generally determine the longest span for common building dimensions. For this example, we will assume a typical height (like 2.5 m):

   $$ L = \frac{2.5 , \text{m}}{\sin(25^\circ)} $$

4. Calculate the Span Length

   Using a calculator, find ( \sin(25^\circ) ):

   $$ L \approx \frac{2.5}{0.4226} \approx 5.91 , \text{m} $$

   Round it to match the answer options provided.

5. Select Closest Answer

   Comparing ( 5.91 , \text{m} ) with the given options, the closest value is:

   • ( 5.96 , m )