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Ann [662]
3 years ago
12

In a 30-60-90 triangle, the length of the long leg is 8. Find the length of the hypotenuse.

Mathematics
1 answer:
fiasKO [112]3 years ago
5 0

Answer:

Step-by-step explanation:

In a 30-60-90 triangle, the ratio of the lengths of the angles' opposite sides are <em>1-√3-2</em>.

If the long leg is 8, then the short one is 8/√3, or <em>8√3/3</em>.

Therefore, the hypotenuse, which is <em>double the short leg</em>, is 16√3/3.

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Find the measure of the arc or angle indicated
MariettaO [177]
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Comment

Any two angles that have their end points on the same end points as a chord and both moving away in the same direction (in this case  down ) are equal. This is a fundamental fact about circles.

Equation
2x + 55 =  x + 55
the only way this is going to make any sense is if x = 0. No other value is possible because it will destroy the equality.

Conclusion
Both angles = 55

But that's not what you are asked for.

What you are asked for
You want to know the measure of arc LM.  
The angle connecting the center of the circle with its two arms running through the end points of the chord = the measure of  arc LM

Draw a dot where the center of the circle is and call it O. Draw in <MOL 
<MOL = 2* either of the 55° = 2 (<LKM)  = 2 * 55 = 110° That's a property of the central angle.

The measure of arc LM = 110°
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3 years ago
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