A13 foot ladder is leaning against a wall. if the point where the ladder meets the wall is 12 feet above the ground, how far from the base of the wall is the the ladder?

5feet

Step-by-step explanation:

A ladder leaning against the wall will form a set up like a right angled triangle since the wall is at 90° to the ground. A right angled triangle consists of 3sides which are the hypotenuse (the longest side), the opposite (the angle facing the acute angle given) and the third angle will be the adjacent.

According to Pythagoras theorem, the sum of the square of the opposite and the adjacent is equal to the square of the hypotenuse. Mathematically;

Hyp² = Opp²+Adj²

Since the ladder which is 13feets leans against the wall, the length of the ladder will serve as the hypotenuse. The point where the ladder meets the wall above the ground is the height if the wall which is the opposite

Opposite= 12feets

The Adjacent will be the distance from the foot of the ladder to the wall say 'x'feet. Using the Pythagoras theorem to get the third side will give;

13² = 12²+x²

x² = 13²-12²

x² = 169-144

x² = 25

x= √25

x = 5feet

This shows that the ladder is 5feet far from the base of the wall.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

3 1/3 x 2 3/5 = 8 2/3

step-by-step explanation:

just multiply the first number by the second number to get your answer.