Answer:
The height of the dog house = 4 feet.
Step-by-step explanation:
Given:
The shape of the dog house is like a tent.
The slant heights of the house is 5 feet.
The bottom of the house is 6 feet across.
To find the height of the dog house at its tallest point.
Solution:
On drawing the figure of the dog house in the shape of a tent, we find out that the tallest point would be at the midpoint of the bottom of the house.
Thus, we ave a right triangle, of which one leg = [tex]\frac{6\ ft}{2}=3\ ft[/tex] and hypotenuse = [tex]5\ ft[/tex]
Applying Pythagorean theorem to find the measure of the other leg which is the height of the house.
[tex]Hypotenuse^2=Leg1^2+Leg2^2[/tex]
Plugging in values.
[tex]5^2=3^2+Leg2^2[/tex]
[tex]25=9+Leg2^2[/tex]
Subtracting both sides by 9.
[tex]25-9=9-9+Leg2^2[/tex]
[tex]16=Leg2^2[/tex]
Taking square root both sides.
[tex]\sqrt{16}=\sqrt{Leg2^2}[/tex]
[tex]4=Leg2[/tex]
Thus, the height of the dog house = 4 feet.
