Fill in the blanks!

Question

A tree is 50 feet tall. At one point during the day, the three casts a shadow on the ground. The distance from the top of the tree to the furthest tip of the shadow is 80 feet. What is the length of the shadow? Round to the nearest hundredth.

Traingle: _ft , 50 ft , a

a^(2) + b^(2) = c^(2)
a^(2) + _^(2) = _^(2)
a^(2) + 2500 = _
a^(2) = _
\sqrt(a^(2) = \sqrt(3900)
a = \sqrt(_)
a ~ _ feet

Answer 1

Given the problem, we have a right triangle where:

• The height of the tree (one leg of the triangle) is 50 ft.
• The distance from the top of the tree to the tip of the shadow (the hypotenuse) is 80 ft.
• We need to find the length of the shadow (the other leg of the triangle).

We can fill in the blanks as follows:

Triangle: a ft, 50 ft, 80 ft

Using the Pythagorean theorem:

1. \( a^{2} + b^{2} = c^{2} \)
2. \( a^{2} + 50^{2} = 80^{2} \)
3. \( a^{2} + 2500 = 6400 \)
4. \( a^{2} = 6400 - 2500 \)
5. \( a^{2} = 3900 \)
6. \( a = \sqrt{3900} \)
7. \( a \approx 62.45 \) feet (rounded to the nearest hundredth)

So, the filled blanks would be:

1. a: 62.45
2. _ : 80
3. _ : 6400
4. _ : 3900
5. _ : 62.45

The final answer: The length of the shadow is approximately 62.45 feet.