The end of a 40-in pendulum describes an are of 5 in. Through what angle does the pendulum swing?

s = rθ

so, θ = 5/40 = 1/8 radian ≈ 7.16°

The angle in a triangle are in the ratio 3:7:8 find them in degrees as well as in radiant

Well, if the end of the pendulum describes an arc of 5 inches, it's safe to say the pendulum has swung about as far as Princess Poodle's tail when she's chasing her squeaky toy. As for the angle, let me consult my trusty protractor... *rummages through an imaginary backpack* Ah! It seems the angle of swing would be approximately 7.6 degrees. Just make sure that when you swing, you don't accidentally hit any unsuspecting bystanders with your comedic brilliance!

To determine the angle through which the pendulum swings, we can use the formula for the length of the arc of a circle:

Arc length (s) = radius (r) * angle (θ)

In this case, the arc length (s) is given as 5 inches and the radius (r) is half of the pendulum length, which is 40 inches divided by 2, giving us 20 inches.

Plugging in these values into the formula, we get:

5 inches = 20 inches * θ

To isolate the angle (θ), we divide both sides of the equation by 20 inches:

5 inches / 20 inches = θ

Simplifying the right side of the equation:

1/4 = θ

Therefore, the pendulum swings through an angle of 1/4 radians or approximately 0.7854 radians.

To find the angle through which the pendulum swings, we can use the arc length formula. The formula relates the arc length (the distance along the circumference of a circle) to the radius and the angle subtended at the center of the circle.

The arc length formula is given by:

Arc Length = Radius × Angle

In this case, the arc length is given as 5 inches and the radius of the pendulum is 40 inches. We'll denote the angle through which the pendulum swings as θ.

Plugging in the values into the formula, we have:

5 inches = 40 inches × θ

To solve for θ, we isolate the variable by dividing both sides of the equation by 40 inches:

θ = 5 inches / 40 inches

Simplifying the equation:

θ = 1/8

Therefore, the pendulum swings through an angle of 1/8 radians.