how to find the length from one end of an object to the other end of a shadow using Pythagoras theorem.
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Answer:
refer the attachment this is the correct answer ☝️
c2 = a2 + b2, where c is the hypothenuse, a is the height, and b is the base of a right triangle.
If we let the height of the tree be represented by x, then the base leg or shadow leg will be x - 14, and the hypothenuse will be x + 2.
Substitute these values in the Pythagorean Theorem gives:
(x + 2)2 = x2 + (x - 14)2
Find the values for (x + 2)2 and (x - 14)2
(x + 2)2 = (x + 2) * (x + 2) = x2 + 4x + 4
(x - 14)2 = (x - 14) * (x - 14) = x2 - 28x + 196
Substitute these values in the given equation:
x2 + 4x + 4 = x2 + x2 - 28x + 196
Combine like terms and set equal to zero.
x2 - 32x + 192 = 0
Solve for x:
We need to find two values when multiplied together equals 192 and when added together = -32.
-1 * -192 = 192, but when added equals -193
-2 * -96 = 192, but when added equals -98
-3 * -64 = 192, but when added equals -67
-4 * -48 = 192, but when added equals -52
-6 * -32 = 192, but when added equals -38
-8 * -24 = 192, and when added equals -32
The solution is:
(x - 8) * (x - 24) = 0
Use the "Zero Product Property" to find x:
x - 8 = 0, x = 8
And
x - 24 = 0, x = 24
We can discard the x = 8 solution because the length of the shadow of the tree would be negative.