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 meters above the ground. What is the height above the ground of the edge of the roof, to the nearest centimeter?
To solve this problem, we can use trigonometry.
First, let's label the given information:
- The angle of the roof slope is 23°.
- The distance from the top of the wall to the edge of the roof is 75 cm.
- The height of the top of the wall above the ground is 5.4 meters.
Now, let's find the height above the ground of the edge of the roof.
Step 1: Convert the height of the wall to centimeters.
The height of the wall is 5.4 meters. Since there are 100 centimeters in a meter, we can convert meters to centimeters by multiplying by 100.
5.4 meters * 100 centimeters/meter = 540 centimeters.
Step 2: Use trigonometry to find the height of the edge of the roof above the ground.
We can use the tangent function, which relates the angle of elevation (23°) to the height and distance. The formula is:
height = distance * tangent(angle)
height = 75 cm * tangent(23°)
Using a calculator, the tangent of 23° is approximately 0.42447.
height = 75 cm * 0.42447
height ≈ 31.83525 cm
Step 3: Add the height of the wall.
To find the total height above the ground, we need to add the height of the edge of the roof to the height of the wall.
total height = height of wall + height of edge of roof
total height = 540 cm + 31.83525 cm
total height ≈ 571.84 cm
Therefore, the height above the ground of the edge of the roof is approximately 571.84 cm (or 572 cm to the nearest centimeter).