Question

13. Oscar's dog house is shaped like a tent. The slanted sides are both 5 feet

Answer 1

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 = $\frac{6\ ft}{2}=3\ ft$ and hypotenuse = $5\ ft$

Applying Pythagorean theorem to find the measure of the other leg which is the height of the house.

$Hypotenuse^2=Leg1^2+Leg2^2$

Plugging in values.

$5^2=3^2+Leg2^2$

$25=9+Leg2^2$

Subtracting both sides by 9.

$25-9=9-9+Leg2^2$

$16=Leg2^2$

Taking square root both sides.

$\sqrt{16}=\sqrt{Leg2^2}$

$4=Leg2$

Thus, the height of the dog house = 4 feet.