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liberstina [14]
3 years ago
7

(15 points)

Mathematics
1 answer:
Maslowich3 years ago
6 0

Answer:

Each of the legs of isosceles right triangle is 5\sqrt{3}

Step-by-step explanation:

Watch the attached figure for the isosceles right angled triangle

Looking at the figure we see that AB=5√6 and BC=CA

According to the Pythagorean theorem the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle.

1) Applying the Pythagorean theorem to the isosceles right triangle, we have

BC^{2} + CA^{2} = AB^{2}

2) Let BC=a and CA=a as they both are equal

So,

a^{2} + a^{2} = (5\sqrt{6} )^{2}

=> 2a^{2} = (5\sqrt{6} )(5\sqrt{6} )

=> 2a^{2} = 5*5*\sqrt{6}*\sqrt{6}

=> 2a^{2} = 25*6 (since √6*√6 = (√6)²= 6)

=> 2a^{2} = 150

3) Dividing both sides by 2, we get

\frac{2a^{2} }{2} =\frac{150}{2}

4) Cancelling out the 2's on the left, we get

a^{2} = 75

5) Taking the square root on both sides, we have

\sqrt{a^{2}} = \sqrt{75}

=> a = 5\sqrt{3}

So,

Each of the legs of isosceles right triangle is 5\sqrt{3}



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Which trigonometric identity can be used to solve for the height of the blue ladder that is leaning against the building?.

<h3>Trigonometric identity</h3>

Trigonometric Identities are the equalities that involve trigonometry functions and hold true for all the values of variables given in the equation.

Trig ratios help us calculate side lengths and interior angles of right triangles:

The trigonometric identity that can be used to solve for the height of the blue ladder is;

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To know more about trigonometric identity click the link given below.

brainly.com/question/1256744

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