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Mathematics

1 answer:

Marina86 [1]2 years ago

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Based on the inscribed quadrilateral conjecture: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

<h3>What is the Inscribed Quadrilateral Conjecture?</h3>

The inscribed quadrilateral conjecture states that the opposite angle of any inscribed quadrilateral are supplementary to each other. That is, they have a sum of 180 degrees.

From the diagram given, the opposite angles in the trapezoid, 115 + 65 = 180 degrees.

Therefore, we can conclude that: trapezoid QPRS can be inscribed in a circle because its opposite angles are supplementary.

Learn more about the inscribed quadrilateral conjecture on:

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HELPPP!! which of the following could be the ratio between the lengths of two legs of a 30,60,90 triangle

sp2606 [1]

Answer:

$\sqrt{3}:3\\1:\sqrt{3}$

Step-by-step explanation:

<u>Trigonometric Ratios</u>

The ratios of the sides of a right triangle are called trigonometric ratios. There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant, and cotangent.

The longest side of the triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The tangent ratio is defined as:

$\displaystyle \tan\theta=\frac{\text{opposite leg}}{\text{adjacent leg}}$

The cotangent ratio is defined as:

$\displaystyle \cot\theta=\frac{\text{adjacent leg}}{\text{opposite leg}}$

As shown above, the tangent and the cotangent are the ratios of the two legs in any possible order.

If the triangle has angles of 30°, 60°, and 90°, then we can take one of the acute angles and find the tangent and cotangent to know the required ratios:

Let's take for example the 30° angle:

$\displaystyle \text{ratio of legs: }\tan 30^\circ=\frac{\sqrt{3}}{3}$