# Chapter 21: Chapter 21

Problem 410

A chord, 16 inches long, is 6 inches from the center of a circle. Find the length of the radius of the circle.

Problem 412

In a right triangle, the length of the hypotenuse is 20 and the length of one leg is \(16 .\) Find the length of the other leg.

Problem 413

Find the length of the diagonal of a rectangle whose sides are \((\sqrt{5})\) inches and 2 inches, respectively.

Problem 415

In a circle, angle \(\mathrm{ABC}\), formed by diameter \(\underline{\mathrm{AB}}\) end chord \(\underline{\mathrm{BC}}\), is \(30^{\circ}\). If the length of the diameter of the circle is 20 , find the length of chord \(\underline{\mathrm{AC}}\) and, in radical form, the length of chord \(\underline{B C}\),

Problem 417

An equilateral triangle has sides of 8 inches. What is its height?

Problem 418

Which of the following are Pythagorean Triples? (a) \(1,2,3 ;\) (b) \(3,4,5 ;\) (c) \(5,6,7 ;\) (d) \(5,12,13\) (e) \(11,60,61 ;\) (f) \(84,187,205\).

Problem 420

A 25 -foot ladder leans against a wall such that the top of the ladder is y feet from the ground, and the base of the ladder is \(x\) feet from the wall. The base of the ladder slides another 17 feet from the wall so that the base is now y feet from the wall and the top is \(\mathrm{x}\) feet from the ground. Find \(\mathrm{y}\), the original height that the ladder reached.

Problem 421

Show that if \(\mathrm{d}\) is the length of a diagonal of a rectangular solid in which every pair of intersecting edges is perpendicular, then \(\mathrm{d}^{2}=\mathrm{a}^{2}+\mathrm{b}^{2}+\mathrm{c}^{2}\), where \(\mathrm{a}, \mathrm{b}\), and \(\mathrm{c}\) are the lengths of the edges.