10. Let’s understand what measurements are what:
The ladder leaning on the wall will form the hypotenuse, so our hypotenuse is 24ft.
The length away from the house to the base of the ladder is one side length of 13ft.
Let’s use Pythagorean’s Theorem to find the height of the wall:
a^2 + b^2 = c^2
c = 24
b = 13
Let’s isolate what we want to solve for, a:
a^2 = c^2 - b^2
a = sqrt( c^2 - b^2 )
Plug in our c and b values:
a = sqrt( (24)^2 - (13)^2 )
a = sqrt( 576 - 169 )
a = sqrt( 407 )
a = 20.17
a = 20.2 ft
The ladder will reach 20.2 ft up the wall of her house.
11. Let’s first find Will’s distance:
a^2 + b^2 = c^2
a = 40
b = 40
c = sqrt( (40)^2 + (40)^2 )
c = sqrt ( 1600 + 1600 )
c = sqrt ( 3200 )
c = 56.6 yards
Now James’ distance:
a^2 + b^2 = c^2
a = 25
b = 35
a = sqrt( (25)^2 + (35)^2 )
a = sqrt( 625 + 1225 )
a = sqrt( 1850 )
a = 43.0 yards
Will ran a longer distance since 56.6 yards is longer than 43.0 yards.