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2 years ago

Triangle △ABC is reflected across line n to create △ A'B'C', What is the measure of ∠C?

Mathematics

1 answer:

Ilya [14]2 years ago

6 0

The measure of ∠C is 54°.

<h3>To solve the problem :</h3>

let us assume that line n is a mirror.

∴ ∠A = ∠A' = 59°

∠B = ∠B' = 67°

∠C = ∠C'

According to property of triangles :

Sum of all angles of a triangle is 180°.

∴ A + B + C = 180°

59 + 67 + C = 180

C = $180 - (59 +67)$

C = 54°

<h3>∴ The measure of ∠C is 54°.</h3>

To know more about triangles refer to :

brainly.com/question/1620555

#SPJ2

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<h2>option b. 52, 48 and 20</h2>

Step-by-step explanation:

<u>let's solve:-</u>

To test whether given this triangle is right triangle or not, we can use the Pythagorean Theorem .

soo

Pythagorean Theorem=

$\bold \green{(leg1)^{2} +(leg2)^{2} =(hypotenuse)^{2} }$

Here:-

$\bold \blue{leg \: 1 = 48} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold \blue{ leg2 = 20} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \bold\blue{hypotenuse = 52}$

Putting values:-

${48}^{2} + {20}^{2} = {52}^{2} \: \: \: \: \: \: \\ \\ 2304 + 400 = 2704 \\ \\ 2704 = 2704 \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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2 years ago

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3 years ago

What is the square root of 864

skelet666 [1.2K]

There are two ways to evaluate the square root of 864: using a calculator, and simplifying the root.

The first method is simplifying the root. While this doesn't give you an exact value, it reduces the number inside the root.

Find the prime factorization of 864:

$\sqrt{864} = \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3}$

Take any number that is repeated twice in the square root, and move it outside of the root:

$\sqrt{864} = \sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3}$

$\sqrt{2 \cdot 2} = \sqrt{4} = 2$

$\sqrt{3 \cdot 3} = \sqrt{9} = 3$

$\sqrt{(2 \cdot 2) \cdot (2 \cdot 2) \cdot 2 \cdot (3 \cdot 3) \cdot 3} = \sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3}$

$\sqrt{(4) \cdot (4) \cdot 2 \cdot (9) \cdot 3} = (2 \cdot 2 \cdot 3) \sqrt{2 \cdot 3} = \boxed{12 \sqrt{6}}$

The simplified form of √864 will be 12√6.

The second method is evaluating the root. Using a calculator, we can find the exact value of √864.

Plugged into a calculator and rounded to the nearest hundredths value, √864 is equal to 29.39. Because square roots can be negative or positive when evaluated, this means that √864 is equal to ±29.39.

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