Question

a hiker wants to determine the height of a tree. she measures the trees shadow to be 29.9 meters long. her own shadow at the same time is 2.6 meters long. if the hiker is 1.9 meters tall, how tall is the tree?

the height of the tree is approximately □ meters.
(type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Set up proportion

Let $h$ = tree height. Proportion: $\frac{h}{29.9} = \frac{1.9}{2.6}$

Step2: Solve for $h$

Multiply both sides by 29.9: $h = \frac{1.9 \times 29.9}{2.6}$

Step3: Calculate the value

$h = \frac{56.81}{2.6} \approx 21.85$

Step4: Round to nearest tenth

$h \approx 21.9$

Answer:

21.9