The shadow of a meter stick measures 1.2m long. At the same time, a nearby tree casts a shadow that is 21.4m long. How tall is the tree?

Identify similar triangles: Identify the similar triangles. The meter stick and its shadow form a right-angled triangle, as does the tree and its shadow. Since the sun's rays are parallel, the triangles are similar, which means the ratios of their corresponding sides are equal.Set up proportion: Set up the proportion using the corresponding sides of the similar triangles. Let the height of the tree be $ h $ meters. The ratio of the height of the meter stick to its shadow is equal to the ratio of the height of the tree to its shadow. So, we have $ \frac{1}{1.2} = \frac{h}{21.4} $.Solve for height: Solve the proportion for $ h $ to find the height of the tree. Cross-multiply to solve for $ h $: $ 1 \times 21.4 = 1.2 \times h $ $ 21.4 = 1.2h $Divide to isolate height: Divide both sides of the equation by 1.2 to isolate $ h $. $ \frac{21.4}{1.2} = h $ $ h \approx 17.8333 $ meters

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The shadow of a meter stick measures $1.2\,\text{m}$ long. At the same time, a nearby tree casts a shadow that is $21.4\,\text{m}$ long. How tall is the tree?

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Q. The shadow of a meter stick measures

1.2\,\text{m}

long. At the same time, a nearby tree casts a shadow that is

21.4\,\text{m}

long. How tall is the tree?

Identify similar triangles: Identify the similar triangles. $\newline$ The meter stick and its shadow form a right-angled triangle, as does the tree and its shadow. Since the sun's rays are parallel, the triangles are similar, which means the ratios of their corresponding sides are equal.
Set up proportion: Set up the proportion using the corresponding sides of the similar triangles. $\newline$ Let the height of the tree be $h$ meters. The ratio of the height of the meter stick to its shadow is equal to the ratio of the height of the tree to its shadow. $\newline$ So, we have $\frac{1}{1.2} = \frac{h}{21.4}$ .
Solve for height: Solve the proportion for $h$ to find the height of the tree. $\newline$ Cross-multiply to solve for $h$ : $\newline$ $1 \times 21.4 = 1.2 \times h$ $\newline$ $21.4 = 1.2h$
Divide to isolate height: Divide both sides of the equation by $1$ . $2$ to isolate $h$ . $\newline$ $\frac{21.4}{1.2} = h$ $\newline$ $h \approx 17.8333$ meters