Pythagorean theorem

Problem 10
In a triangle ABC, if   $\dfrac{2 \cos A}{a} + \dfrac{\cos B}{b} + \dfrac{2 \cos C}{c} = \dfrac{a}{bc} + \dfrac{b}{ca}$,   find the value of angle $A$.
 

Problem 10
A boy on a bike rides north 5 mi, then turns east (Fig. 47). If he rides 10 mi/hr, at what rate does his distance to the starting point S changing 2 hour after he left that point?
 

Problem 06
A ladder 20 ft long leans against a vertical wall. If the top slides downward at the rate of 2 ft/sec, find how fast the lower end is moving when it is 16 ft from the wall.
 

In reference to the right triangle shown and from the functions of a right triangle:
a/c = sin θ
b/c = cos θ
c/b = sec θ
c/a = csc θ
a/b = tan θ
b/a = cot θ
 

Pythagorean Theorem
In any right triangle, the sum of the square of the two perpendicular sides is equal to the square of the longest side. For a right triangle with legs measures $a$ and $b$ and length of hypotenuse $c$, the theorem can be expressed in the form