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Help! special triangles

Help! special triangles-example-1

1 Answer

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Answer:

x = y = 8

Explanation:

We presume you want the values of x and y.

The angle not shown is also 45°, as the two acute angles are complementary. Then the triangle isosceles and x = y.

If you need to, you can use the Pythagorean theorem to find the value of x (and y).

(8√2)² = x² + x²

128 = 2x² . . . . simplify

64 = x² . . . . . . divide by 2

8 = x . . . . . . . . positive square root

The values of x and y are both 8.

_____

Hopefully, you will memorize the side ratios of an isosceles right triangle. They are ...

1 : 1 : √2

Multiplying these numbers by 8 gives ...

x : y : 8√2 = 8 : 8 : 8√2

In short, recognizing the factor of √2 in the number on the hypotenuse, you know immediately the values of x and y are both 8 in this 45°-45°-90° triangle.

User Mvera
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