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2 years ago

10

Consider the rectangle shown

1 answer:

emmainna [20.7K]2 years ago

8 0

Step-by-step explanation:

<em>Perimeter </em><em>of </em><em>a </em><em>rectangle</em><em>=</em><em> </em><em>2</em><em>L</em><em> </em><em>+</em><em> </em><em>2</em><em>W</em>

<em>let </em><em>the </em><em>length </em><em>be </em>2x-1<em> </em><em>and </em><em>breadth</em><em>/</em><em> </em><em>width </em><em>=</em><em> </em>3x+5

52= 2x-1 + 3x+5

52= 5x +4

<em> </em><em>collect </em><em>like </em><em>terms</em><em>;</em>

52-4 = 5x

48=5x

<em>divide </em><em>by </em><em>the </em><em>co- </em><em>efficient </em><em>of </em><em>X</em>

<em>x=</em><em> </em><em>9</em><em>.</em><em>6</em><em>.</em>

<em>hope </em><em>it </em><em>helps.</em><em> </em><em>pls </em><em>like </em><em>and </em><em>follow </em><em>:-)</em><em>:-)</em>

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In ΔABC, ∠C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.

riadik2000 [5.3K]

Answer:

The remaining side and angles are $a = 20\sqrt{3}$ , $\angle A = 60^{\circ}$ and $\angle B = 30^{\circ}$ .

Step-by-step explanation:

According to the information given on statement, we are in front of a right triangle because $\angle C$ , opossite to side $c$ , is a right angle. Hence, $c$ is the hypotenuse of the right triangle and $b$ , a leg. The missing length can be calculated by the Pythagorean Theorem:

$a = \sqrt{c^{2}-b^{2}}$ (1)

If we know that $c = 40$ and $b = 20$ , then the length of the missing leg is:

$a = \sqrt{c^{2}-b^{2}}$

$a = 20\sqrt{3}$

Lastly, we find the value of the missing angles by means of direct and inverse trigonometric relations:

Angle A

$\angle A = \tan^{-1}\left(\frac{a}{b} \right)$ (2)

Angle B

$\angle B = \tan^{-1} \left(\frac{b}{a} \right)$ (3)

If we know that $a = 20\sqrt{3}$ and $b = 20$ , then the values of the missing angles are, respectively:

Angle A

$\angle A = \tan^{-1}\left(\frac{a}{b} \right)$

$\angle A = 60^{\circ}$

Angle B

$\angle B = \tan^{-1} \left(\frac{b}{a} \right)$

$\angle B = 30^{\circ}$

The remaining side and angles are $a = 20\sqrt{3}$ , $\angle A = 60^{\circ}$ and $\angle B = 30^{\circ}$ .

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Could y'all help with this? :]

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