Monique made a scale drawing of her triangular vegetable garden. Two sides of te garden are 7m and 9m. The angle between these sides is 75 degrees. Monique's drawing was a triangle with side lengths 14.0cm and 18.0cm, with an angle of 75 degrees between them. She drew the third side, then measuired it. It was 19.7cm long. What is the length of the third side of the vegetable garden?
you have 2 similar triangles
the ratio of the numerical values of corresponding sides of the scale model to the actual garden is 2:1
Since the side in the scale model is 19.7 cm, the side in the garden would have to be 9.85 or 9.9 m.
(actually we could have just used the cosine law to find the third side of the garden
x^2 = 7^2 + 9^2 - 2(7)(9)cos 75º
x^2 = 97.3888
x = √97.3888 = 9.87 or 9.9 m )
A triangle has side lenghts of 27 inches,54 inches and 72 inches.Wich list shows the side lenghths of a simillar triangle ?? A.3inches,6inches,8inches B.9inches,36inches,45inches C.9inches,18inches,16inches D.18inches,27inches,54inches
To find the length of the third side of the vegetable garden, we can use the concept of similar triangles. The lengths and angles in the scale drawing can be proportional to the actual lengths and angles of the vegetable garden.
Let's set up a proportion using the given information:
Length of the actual third side / Length of the corresponding side in the scale drawing = Length of the other actual side / Length of the corresponding side in the scale drawing
Let's substitute the known values into the proportion:
Length of the actual third side / 19.7 cm = 9 m / 18.0 cm
We need to convert the 9 m to centimeters, so multiply by 100:
Length of the actual third side / 19.7 cm = 9 m * 100 / 18.0 cm
Simplifying the equation:
Length of the actual third side / 19.7 cm = 900 cm / 18.0 cm
Now, cross-multiply:
Length of the actual third side * 18.0 cm = 19.7 cm * 900 cm
Dividing both sides by 18.0 cm:
Length of the actual third side = (19.7 cm * 900 cm) / 18.0 cm
Calculating:
Length of the actual third side = 19.7 cm * 50
Length of the actual third side = 985 cm
Therefore, the length of the third side of the vegetable garden is 985 cm.