Question

Please help me find x, y, and z

Answer 1

9514 1404 393

Answer:

• x = 4
• y = 45
• z = 4

Explanation:

Since this is a right triangle, the acute angles are complementary.

y° = 90° -45°

y° = 45°

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The two acute angles are congruent, so the triangle is isosceles. That is, x = z. The Pythagorean theorem tells you the relation between the sides of the triangle:

x² + z² = (4√2)²

x² +x² = 4²×2 . . . substitute x for z, since they are equal

x² = 4² . . . . . . . divide by 2

x = 4 . . . . . . . . .take the positive square root

z = 4 . . . . . . . . same as x

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Additional comment

Whenever you see a 45° angle in a right triangle you know immediately that it is isosceles, and that the ratios of the side lengths are 1 : 1 : √2. This is one of two "special" triangles that have angles and side ratios that are not difficult to remember.

The hypotenuse here is 4√2, so the other sides are 4.

x : z : 4√2 = 1 : 1 : √2 = 4 : 4 : 4√2

x = z = 4