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Shkiper50 [21]
3 years ago
10

Find the hypotenuse of each isosceles right triangle when the legs are of the given measure. 6 sqrt 2

Mathematics
1 answer:
Gemiola [76]3 years ago
7 0
Isosceles right triangles have two equal sides (a and b) that are not the hypotenuse (c). And when two sides are equal, so are their opposite angles. There are only 180° degrees in any triangles, thus the right angle = 90°, so 90 left for the two equal, means that 2x=90,
x = 45°.

There are several ways to go about solving a triangle like this. The best and easiest is simply to memorize that the hypotenuse is exactly root2 times the other sides. Or, each isosceles side is the hypotenuse (c) ÷ root2
a = b = c \div  \sqrt{2} \\ c  = a\sqrt{2}  \\ c = 6 \sqrt{2} \times \sqrt{2}  = 6 \times 2 = 12
Another way to do it is the longer proof of Pythagorean Theorem:
{c}^{2}  =  {a}^{2}  +  {b}^{2}... \:  \:  c =   \sqrt{({a}^{2}  +  {b}^{2})}  \\
c= \sqrt{({6 \sqrt{2}) }^{2} + ({6 \sqrt{2})}^{2}}  \\ =  \sqrt{(2 \times{(6 \sqrt{2} )}^{2} )}  =  \sqrt{2(36 \times 2)}  \\ c =  \sqrt{144}  = 12

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Step-by-step explanation:

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A state university locks in costs for a student once a student starts attending the university. The total cost is $23,500. A stu
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What is the following product 3 sqrt 2(5 sqrt 6-7 sqrt 3)
Licemer1 [7]
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Find the solution of the system of equations. 6x -y= 21. -5x + y= -18​
Lapatulllka [165]
First one is -6 and the second one is -3
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2 years ago
Alex is 1.6 m tall and Noah is 1.5 times as tall as Alex how much taller is Noah in cm
Andrew [12]
<span>Alex is 1.6 m tall
and
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1 m = 100 cm
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answer
Noah is 240 cm</span>
3 0
3 years ago
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