Loving life, this is the solution to the problem:
Step 1: Let's use the Therorem, as follows:
c² = a² + b²
Where,
• x represents the height of the tree
,
• x + 2 represents the shadow of the tree
,
• 18 represents the hypotenuse (distance from the top of the tree to the tip of the shadow)
Therefore,
18² = x² + (x + 2)²
324 = x² + x² + 4x + 4
0 = 2x² + 4x - 320
Dividing by 2 at both sides:
0 = x² + 2x - 160
x = (-2 +/- √2² - 4 * 1 * - 160)/2
x = (-2 +/- √4 + 640)/2
x = (-2 +/- √644)/2
x = (-2 +/- 25.38)/2
x1 = -27.38/2
x2 = 23.38/2
x1 = - 13.69
x2 = 11.69
We take x2 because the height of a tree can't be a negative value.
Therefore,
the height of the tree is 11.69 feet
the shadow of the tree is 13.69 feet