I need help with this ASAP!!

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5. What

krok68 [10]

The area of the required triangle is 9/π²(3 + √3) sq. units.

In the question, we are given that a triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of lengths 3, 4, and 5.

We are asked for the area of the triangle.

Now, the circumference of the circle = 3 + 4 + 5 = 12 units.

The formula for the circumference is 2πr, which gives is:

2πr = 12,

or, r = 6/π.

The length of the arcs are proportional to its central angle, making the angles: 3θ, 4θ, and 5θ, which needs to sum up to 360°, giving us θ = 360°/12 = 30°.

Thus, the three arcs subtends angles of θ₁ = 3θ = 90°,θ₂ = 4θ = 120°, and θ₃ = 5θ = 150°.

The area of the circle can be calculated as:

Area = (1/2)r² sin θ₁ + (1/2)r² sin θ₂ + (1/2)r² sin θ₃ = r²/2(sin θ₁ + sin θ₂ + sin θ₃).

Substituting the values, we get:

Area = 36/2π²(sin 90° + sin 120° + sin 150°),

or, Area = 36/2π²( 1 + √3/2 + 1/2),

or, Area = 9/π²(3 + √3).

Thus, the area of the required triangle is 9/π²(3 + √3) sq. units.

Learn more about a triangle at

brainly.com/question/13734546

#SPJ4

5 0

1 year ago

Which relationship describes angles 1 and 2?

Vikki [24]

Vertical angels is the answer

8 0

2 years ago

The yellow cube shows a multiple of 3 given that the product is 6

Fynjy0 [20]

Need more information to be answered

3 0

2 years ago

What is the answer to this question

Gre4nikov [31]

4x^2 -2x +3
mark me as brainliest if i’m right !

5 0

3 years ago

On average, it takes a shoe factory 21 minutes, with a standard deviation of 3 minutes, to manufacture a pair of running shoes.

algol13

Answer:

The number of times it would take more than 27 minutes to manufacture a pair of running shoes is 2.275 times or approximately 2 times per every 100 shoes

Step-by-step explanation:

The average time it takes to manufacture a pair of shoes = 21 minutes;

The standard deviation = 3 minutes

To find how often it takes more than 27 minutes to manufacture a pair of running shoes, we have;

Standard score, given as follows;

$Z=\dfrac{x-\mu }{\sigma }$

Where;

x = The raw score = 27 minutes

μ = The average score = 21 minutes

σ = The standard deviation = 3 minutes

From which we have;

$Z=\dfrac{27-21 }{3 } = 2$

Therefore, it is borderline unusual with a p value of P(z>2) = 1 - 0.97725 = 0.02275

Therefore, the number of times out of 100 that it would take more than 27 minutes to manufacture a pair of running shoes = 100 × 0.02275 = 2.275 times which is approximately 2 times in every 100 shoes.

7 0

3 years ago