What is the relationship between the sides of a right triangle?

Mathematics

1 answer:

siniylev [52]3 years ago

4 0

Answer:

⇒ $(Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2$ is the required relationship.

Step-by-step explanation:

Let us assume, the given right angled triangle is ΔPQR.

Here. PQ = Perpendicular of the triangle.

QR = Base of the triangle.

PR = Hypotenuse of the triangle.

Now, PYTHAGORAS THEOREM states:

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“

⇒ $(Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2$

Hence in ΔPQR: $(QR)^2 + ( PQ)^2 = (PR)^2$

And the above expression is the required relationship between the sides of a right triangle.

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3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round

Mariana [72]

The volume of the prop is calculated to be 2,712.96 cubic inches.

<u>Step-by-step explanation:</u>

Step 1:

The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2:

The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 9 inches and the height is 14 inches.

The volume of the cone : $V=\pi r^{2} \frac{h}{3}$ = $3.14 \times 9^{2} \times \frac{14}{3}$ = 1,186.92 cubic inches.

Step 3:

The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).