Use the Pythagorean theorem: a² + b² = c². So 12² + 5² = 144 + 25 = 169. √169 = 13 feet.
7² + 24² = 49 + 576 = 625 = 25². Since a² + b² = c², it is a right triangle.
For a square with side s, the diagonal = s√2. So s√2 = 10√2, meaning s = 10 cm.
d = √((6−2)² + (6−3)²) = √(16 + 9) = √25 = 5.
Perpendicular slopes are negative reciprocals. The negative reciprocal of 3/4 is −4/3.
The contrapositive reverses and negates both parts: "If the ground is not wet, then it does not rain." A contrapositive always has the same truth value as the original.
Alternate interior angles are congruent when formed by parallel lines and a transversal. So the other angle is also 65°.
Vertical angles are always congruent. The other angle is also 48°.
Multiply each side by the scale factor: 3×3=9, 4×3=12, 5×3=15.
By the Triangle Proportionality Theorem: AD/DB = AE/EC → 6/4 = 9/EC → EC = 9 × 4/6 = 6.
In a 45-45-90 triangle, hypotenuse = leg × √2. So 8√2 ≈ 11.31.
The sum of angles in a triangle is 180°. ∠C = 180° − 55° − 65° = 60°.