Answer:
The height of his dog house at its tallest point is 4 feet.
Step-by-step explanation:
From the analysis of the problem, the phrase "the slanted sides are both 5 feet long" gives us a hint that the dog house's shape is an isosceles triangle.
To know where is the height of the triangle, we draw the isosceles triangle and put a line from the vertex of the equal sides down to the base.
I provided an image for your reference. From the image below, the "a" represent the equal sides, the "h" stands for the height of the triangle, and "b" is the base.
Also, from the illustration, upon drawing the height (h), we can form a right triangle. We can use the Pythagorean Theorem to get the height.
Pythagorean theorem → c² = a² + b²
Since our reference illustration also have a and b, to avoid confusion, we can replace the letters/ variables in the Pythagorean Theorem.
Our working equation (based on the right triangle formed from the isosceles triangle in the image below) will be
a² = h² + ([tex]\frac{b}{2}[/tex])²
**Note that the base of the right triangle is only half of the base of the isosceles triangle that is why we use [tex]\frac{b}{2}[/tex].
Solution:
- a = 5 ft
- b = 6 ft
- [tex]\frac{b}{2}[/tex] = 3 ft
- a² = h² + ([tex]\frac{b}{2}[/tex])²
- h = [tex]\sqrt{(a)^2 - (b/2)^2}[/tex]
- h = [tex]\sqrt{(5 ft)^2 - (3 ft)^2}[/tex]
- h = [tex]\sqrt{25 ft - 9 ft}[/tex]
- h = [tex]\sqrt{16 ft}[/tex]
- h = 4 ft
Therefore, the height of his dog house at its tallest point is 4 feet.
Learn more about Pythagorean Theorem here:
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