The eaves of a roof sloping at 23° overhand the walls, the edge of the roof being 75 cm from the top of the wall. The top of the wall is 5.4 metres above the ground. What is the height above the ground of the edge of the roof, to the nearest centimeter?
If I am picturing this correctly, a right triangle is formed, with the hypotenuse c = 75 cm.
Since the top of the wall is 5.4 m above ground, 5.4 - side a = height above ground to the roof edge.
Angle A = 180 - (23 + 90) = 82 degrees
sin 82 = op/hyp = a/c = a/75
0.9903 = a/75
a = 74 cm
5.4 m /100 = 540 cm
540 cm - 74 cm = 466 cm
466 cm = height above ground to roof edge
To solve this problem, we need to find the height above the ground of the edge of the roof.
Let's break down the given information:
- The eaves of a roof sloping at 23° overhang the walls.
- The edge of the roof is 75 cm from the top of the wall.
- The top of the wall is 5.4 meters above the ground.
We can start by visualizing the situation described. Imagine a right-angled triangle with two sides: one representing the height from the ground to the top of the wall (5.4 meters) and the other representing the distance between the top of the wall and the edge of the roof (75 cm).
Now, we need to find the length of the hypotenuse, which represents the height above the ground of the edge of the roof. To find this, we can use trigonometry.
In the given problem, the angle of elevation is given as 23°, and we know the adjacent side (75 cm) and the hypotenuse (which is the height above the ground that we're trying to find).
To find the height, we can use the formula: The height = adjacent side / tan(angle of elevation).
Calculating this, we have: The height = 75 cm / tan(23°).
Using a calculator, tan(23°) is approximately 0.4245.
Now, we can calculate the height:
The height = 75 cm / 0.4245 ≈ 176.63 cm.
Since the question asks for the answer in centimeters, the height above the ground of the edge of the roof is approximately 176.63 cm or 177 cm when rounded to the nearest centimeter.