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tensa zangetsu [6.8K]
3 years ago
14

Find the exact values of x and y.

Mathematics
1 answer:
wlad13 [49]3 years ago
8 0

Given:

θ = 60°

Opposite side of θ = 6

Adjacent side of θ = x

Hypotenuse = y

To find:

The value of x and y.

Solution:

Using basic trigonometric ratio formula:

$\tan\theta =\frac{\text{Opposite side of } \theta}{\text{Adjacent side of } \theta}

$\tan60^\circ=\frac{6}{x}

The value of tan 60° = √3

$\sqrt{3} =\frac{6}{x}

Multiply by x on both sides.

$\sqrt{3} \times x=\frac{6}{x} \times x

$\sqrt{3} \times x=6

Divide by √3 on both sides, we get

$\frac{\sqrt{3} \times x}{\sqrt{3} } =\frac{6}{\sqrt{3} }

x=2\sqrt{3}

Using Pythagoras theorem:

\text{Hypotenuse}^2 = \text{Opposite}^2 + \text{Adjacent}^2

y^2 = 6^2 +({2\sqrt {3}})^2

y^2 = 36  +12

y^2 = 48

Taking square root on both sides, we get

y=4 \sqrt{3}

Therefore, the exact values of x and y are x=2 \sqrt{3}, y=4 \sqrt{3}.

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The area of the shaded region = area of larger circle - area of smaller circle = 423.9 yd².

<h3>What is the Area of a Circle?</h3>

Area = πr²

Area of the shaded region = area of larger circle - area of smaller circle

Area of larger circle = πr² = (3.14)(16²) = 803.84 yd²

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pliz mark my answer brainliest

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Step-by-step explanation:

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+10             +10

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