A14 foot ladder is leaning against a building. the ladder makes a 45 degree angle with the building. how far up the building does the ladder reach?

The answer is 9.9 ft.

Imagine that the ladder is a hypotenuse of a right triangle (since ground and the building form a right angle). The sum of angles in a triangle is 180°. If we have:
90° + 45° + x° = 180°
135° + x = 180°
x = 45°

Since two angles are the same this is isosceles triangle a = b.

Use the Pythagorean theorem:
a² + b² = c²
a = b
a² + a² = c²
2a² = c²

c = 14 ft
2a² = 14²
2a² = 196
a² = 196/2 = 98
a = √98 ≈ 9.9 ft

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