Two trees cast a shadow when the sun is up. The shadow of one tree is 15 m long. The shadow of the other tree is 8.3 m long. The shorter tree is 3.5 m tall.
a) Show that the two triangles formed between each tree and it's shadow are similar.
b) Find the height of the taller tree to 1 decimal place.
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Step-by-step explanation:
We can set up a proportion comparing the height of each object to the length of the shadow.
h
s
h
15
=
18
10
Cross multiply
10
⋅
h
=
18
⋅
15
10
h
=
270
Use the multiplicative Inverse
10
h
10
=
270
10
h
=
27
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