Question

a bird is at the very top of a 35 - foot tree. he spies a worm that is 50 feet from the base of the tree. set up a right triangle picture to find the distance from the bird to the worm. round to the nearest whole number.

x = 35.8 × ft

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, if \(a = 35\) (height of the tree) and \(b=50\) (distance from the base of the tree to the worm), and \(c\) is the hypotenuse (distance from the bird to the worm), by the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 35\) and \(b = 50\) into the formula: \(c=\sqrt{35^{2}+50^{2}}\).
First, calculate \(35^{2}=35\times35 = 1225\) and \(50^{2}=50\times50=2500\).
Then \(a^{2}+b^{2}=1225 + 2500=3725\).
So \(c=\sqrt{3725}\).

Step2: Simplify the square - root

\(\sqrt{3725}=\sqrt{25\times149}=5\sqrt{149}\approx5\times12.20655561528 = 61.0327780764\).

Step3: Round to the nearest whole number

Rounding \(61.0327780764\) to the nearest whole number. Since the decimal part \(0.0327780764\lt0.5\), we get \(61\).

Answer:

\(61\)