I will give brainliest!!!!!

Given: ∆ABC, m∠C = 90° CB = 8, m∠B = 38º Find the area of a circumscribed circle. Find the area of the inscribed circle.

vitfil [10]

Answer:

Circumscribed circle: Around 80.95

Inscribed circle: Around 3.298

Step-by-step explanation:

Since C is a right angle, when the circle is circumscribed it will be an inscribed angle with a corresponding arc length of 2*90=180 degrees. This means that AB is the diameter of the circle. Since the cosine of an angle in a right triangle is equivalent to the length of the adjacent side divided by the length of the hypotenuse:

$\cos 38= \dfrac{8}{AB} \\\\\\AB=\dfrac{8}{\cos 38}\approx 10.152$

To find the area of the circumscribed circle:

$r=\dfrac{AB}{2}\approx 5.076 \\\\\\A=\pi r^2\approx 80.95$

To find the area of the inscribed circle, you need the length of AC, which you can find with the Pythagorean Theorem:

$AC=\sqrt{10.152^2-8^2}\approx 6.25$

The area of the triangle is:

$A=\dfrac{bh}{2}=\dfrac{8\cdot 6.25}{2}=25$

The semiperimeter of the triangle is:

$\dfrac{10.152+6.25+8}{2}\approx 24.4$

The radius of the circle is therefore $\dfrac{25}{24.4}\approx 1.025$

The area of the inscribed circle then is $\pi\cdot (1.025)^2\approx 3.298$ .

Hope this helps!

6 0

3 years ago

Using spreadsheets to Organize Data (PLEASE HELP)

katrin [286]

I can give you the first half!
1. D2 - hours worked on monday, 3hrs
2. E2 - money earned on monday, $15
3. D3 - hours worked on tuesday, 3 hrs
4. E3 - money earned on tuesday, $15
5. D4 - hours worked on thursday, 4 hrs
6. E4 - money earned on thursday, $20

6 0

2 years ago

In a study about all terrain vehicle usage, the number of people using 4-wheelers is shown by age group.

DochEvi [55]

Answer:

44-55-0.243

33-37-0.343

6 0

3 years ago

What does the information demonstrate about Alex’s investments? He should have invested in a commodity instead of a stock. He wo

Alekssandra [29.7K]

Answer:

Answer is C.

;) have good day

6 0

3 years ago

Read 2 more answers

Suppose a horticulturist measures the aboveground height growth rate of four different ornamental shrub species grown in a green

torisob [31]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The decision is to reject the null hypothesis at a significant level of significance $\alpha = 0.05$ There is sufficient evidence to conclude that at least one of the population mean is different from at least of the population

Step-by-step explanation:

From the question we are told that the claim is

The mean growth rates of all four species are equal.

The null hypothesis is

$H_o : \mu _1 = \mu_2 = \mu_3 = \mu_4$

Th alternative hypothesis is

$H_a: at \ least \ one \ of \ the \ means \ is \not\ equal$

From question the p-value is $p-value = 0.015$

And since the $p-value < \alpha$ so the null hypothesis will be rejected

So

The decision is to reject the null hypothesis at a significant level of significance $\alpha = 0.05$ There is sufficient evidence to conclude that at least one of the population mean is different from at least of the population

7 0

3 years ago