Bottom part of the greenhouse has a length of 350 cm, width of 220 cm, angle at the peak of the roof measures 90 degrees. Sketch the frame and label it with actual dimensions.
Use trigonometry to find length of the roof pieces. Use a scale of 1:25 to calculate measurements for your scale model.
How to I figure out the new measurements and the length of the roof pieces? Please help! Thanks.
To figure out the new measurements and the length of the roof pieces, we will use trigonometry and the given dimensions of the greenhouse.
First, let's start by sketching the frame of the greenhouse and labeling it with the actual dimensions. Since the angle at the peak of the roof measures 90 degrees, we can visualize the greenhouse as a right-angled triangle.
To do this, draw a rectangle representing the bottom part of the greenhouse with a length of 350 cm and a width of 220 cm. Then, draw a diagonal line cutting the rectangle from one corner to the opposite corner, forming a right-angled triangle. Label the bottom side (base) as 350 cm, the height as 220 cm, and the diagonal (hypotenuse) as "? cm" or "Roof piece".
Now, let's move on to calculating the new measurements using the given scale of 1:25. This means that every 1 cm on the actual greenhouse will be represented by 25 cm on the scale model.
To find the new measurements, we need to multiply the actual dimensions by the scale factor of 25. So, the new length of the bottom part of the greenhouse on the scale model would be 350 cm × 25 = 8750 cm, and the new width would be 220 cm × 25 = 5500 cm.
Next, let's use trigonometry to find the length of the roof pieces. Since we have a right-angled triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we know the lengths of the base (350 cm) and the height (220 cm). Let's call the hypotenuse (roof piece) "c".
Using the Pythagorean theorem, we have the equation: c^2 = 350^2 + 220^2.
To find the value of "c", we need to take the square root of both sides of the equation: c = √(350^2 + 220^2).
Using a calculator, you can calculate the value of "c" to find the length of the roof pieces.
Finally, on your scale model, the length of the roof pieces would be determined by multiplying the calculated length by the scale factor of 25.
Remember to label the lengths of the roof pieces on your sketch and include the units (cm) to indicate the scale model measurements.