In sunlight, a vertical stick 7 ft tall casts a shadow 3 ft long. At the same time, a nearby tree casts a shadow 11 ft long. How tall is the tree? Round to the nearest tenth.
Answer (3)
l oo k a t t h e p i c t u re Δ A BC ∼ Δ D EF ∣ EF ∣ ∣ E D ∣ = ∣ BC ∣ ∣ A B ∣ 11 ∣ E D ∣ = 3 7 / ⋅ 11 ∣ E D ∣ = 3 77 ∣ E D ∣ ≈ 25.7 ( f t ) ← A n s w er
25.7 feet. ;
The height of the tree can be calculated using the proportion of heights to shadow lengths. It is found to be approximately 25.7 feet when rounded to the nearest tenth. This is done using the ratio formed by the similar triangles of the stick and the tree.
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