Question

Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.  ​

Answer 1

Answer:

Height is 12.68 m

Step-by-step explanation:

• Consider triangle formed by Ethan's head, Ethan's feet and shadow's tip

• opposite = 1.85 m
• hypotenuse = x
• adjacent = (28.45 - 24.3) = 4.15 m

• From pythogras theorem:

${ \rm{a {}^{2} + {b}^{2} = {c}^{2} }} \\ { \rm{ {4.15}^{2} + {1.85}^{2} = {x}^{2} }} \\ { \rm{ {x}^{2} = 20.645}} \\ { \rm{x = 4.54}} \\ { \rm{hypotenuse = 4.54 \: m}}$

• From scale factors:

${ \rm{ \frac{28.45}{4.15} = \frac{h}{1.85} }} \\ \\ { \rm{h = \frac{1.85 \times 28.45}{4.15} }} \\ \\ h = 12.68 \: m$

Answer 2

Answer:

• 12.68 m

Step-by-step explanation:

Use the similarity of two triangles.

The ratio of corresponding sides is equal.

Let the height of the tree is x, then we have:

• x / 1.85 = 28.45 / (28.45 - 24.3)
• x / 1.85 = 28.45 / 4.15
• x = 1.85*28.45 / 4.15
• x = 12.68 m (rounded)