Question

On a sunny day, go outside and find an object (that is too large to measure) that is casting a shadow on the ground. Measure the length of the shadow. Find a stick and measure the height of the stick and the shadow it casts. Generate two triangles to show your measurements (either on paper or in word processing software or in a similar picture online). Draw a picture of the triangles. On the picture, write the measurements and the similarity ratio. Provide an explanation about how you calculated the similarity ratio and the final height of the large object.

1) Triangle 1:
- Length of shadow: a
- Height of stick: b
- Height of shadow on stick: c

2) Triangle 2:
- Length of shadow (large object): x
- Height of large object: h

a) a/b = x/h, Similarity Ratio: a/b
b) b/a = h/x, Similarity Ratio:b/a
c) c/a = h/x, Similarity Ratio: c/a
d) x/h = c/a, Similarity Ratio: x/h

Answer 1

To calculate the similarity ratio and the final height of the large object, use two similar triangles: Triangle 1 and Triangle 2.

Step-by-step explanation:

To calculate the similarity ratio and the final height of the large object, we will use two similar triangles: Triangle 1 and Triangle 2. Triangle 1 has a length of shadow (a), height of stick (b), and height of shadow on stick (c). Triangle 2 has a length of shadow for the large object (x) and the height of the large object (h).

To find the similarity ratio between Triangle 1 and Triangle 2, we can use the equation a/b = x/h. This equation shows that the ratio of the length of the shadow to the height of the stick is equal to the ratio of the length of the shadow of the large object to the height of the large object. We can rearrange the equation to find the similarity ratio: x/h = a/b.

To calculate the final height of the large object, we can use the equation x/h = c/a. This equation shows that the ratio of the length of the shadow of the large object to the height of the large object is equal to the ratio of the length of the shadow on the stick to the length of the shadow.