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scoundrel [369]
2 years ago
12

NEED THIS DONE ASAP!! Thank you!!​

Mathematics
1 answer:
bezimeni [28]2 years ago
4 0

Answer:

126°

Step-by-step explanation:

<u>Circle Theorem vocabulary</u>

  • <u>Chord</u>: a straight line joining two points on the circle.
  • <u>Inscribed angle</u>: the angle formed (vertex) when two chords meet at one point on a circle.
  • <u>Arc</u>: the curve between two points on the circumference of a circle
  • <u>Intercepted arc</u>: the arc that is between the endpoints of the chords that form the inscribed angle.

<u>Inscribed Angle Theorem</u>

The measure of an <u>inscribed angle</u> is half the measure of the <u>intercepted arc</u>.

Therefore:

  \displaystyle \angle RST=\dfrac{1}{2} \overset{\frown}{RT}

\implies 63^{\circ}=\dfrac{1}{2} \overset{\frown}{RT}

\implies \overset{\frown}{RT}= 2 \cdot 63^{\circ}

\implies \overset{\frown}{RT}= 126^{\circ}

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<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is 16 \sqrt{3} units.

As all the sides are equal thus the \Delta MNO is a equilateral triangle in which the height of the divides the triangle into two equal part of the length 8\sqrt{3} at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the  \Delta MRN, the length of the hypotenuse is 16 \sqrt{3} units and the length of the base is 8\sqrt{3} units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2

Solve for <em>h,</em>

<em />

<em />\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end<em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

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