Answer:
1: 8 ft
2: 10 cm
3: c is approximately 127.2 or exactly equal to 90 * sqrt(2)
4: sqrt(133)
Step-by-step explanation:
(1) Kevin tries to climb a wall with a ladder. The length of a ladder is 17 feet and it reaches only 15 feet up the wall. What is the distance between the base of the ladder and the wall? :
Here you can use the Pythagorean Theorem to find the length of the base.
the equation is a^2 + b^2 = c^2 where c is the hypotenuse. In this case 17 is the hypotenuse which is c, 15 is a or b it doesn't really matter where you put it.
a^2 + (15)^2 = 17^2
a^2 + 225= 289
a^2 = 64
a = 8
(2) In a right triangle, if the length of one leg is 8 cm and the length of the other leg is 5 cm, what is the length of the hypotenuse? :
The same formula can be used except you don't have to move anything around.
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
10 = c
10 cm
A baseball field is a square with sides of length 90 feet. What is the shortest distance between the first base and the third base?:
So if you look at the image provided, the shortest distance is just a straight line, but more specifically that straight line forms two triangles with the same lengths, That line is the hypotenuse so you can use the same equation as the previous equations
90^2 + 90^2 = c^2
16,200 = c^2
c is approximately 127.2 or exactly equal to 90 * sqrt(2)
(4) How far up a wall will a 13-meter ladder reach, if the foot of the ladder is 6 meters away from the base of the wall?:
6^2 + b^2 = 13^2
36 + b^2 = 169
b^2 = 133
b = sqrt(133)
