World problems
Tom is building a wooden fence in his backyard. He wants to make sure that the corner of the fence forms a right angle. If one side of the fence is 5 feet long and the other side is 12 feet long, how long should the diagonal side be to form a right triangle?
In this case, the two sides of the right triangle are 5 feet and 12 feet. Let's call the length of the diagonal side x.
So, according to the Pythagorean theorem:
\(5^2 + 12^2 = x^2\)
\(25 + 144 = x^2\)
\(169 = x^2\)
Taking the square root of both sides, we get:
\(x = 13\)
Therefore, the length of the diagonal side of the fence should be 13 feet to form a right triangle.
Question: What is the hypotenuse of a right triangle?
The side opposite the right angle.
In a right triangle, if one leg is 5 units long and the other leg is 12 units long, what is the length of the hypotenuse?
Answer: Using the Pythagorean theorem: c = v52 + 122 = V25 + 144 = V169 = 13
units.
A right triangle has one leg measuring 10 meters and the hypotenuse measuring 26 meters. What is the length of the other leg?
Answer: Using the Pythagorean theorem: a = V262 - 102 = V676 - 100 = V576 = 24
meters.
Problem: A ladder is leaning against a wall. If the ladder is 10 feet long and the base of the ladder is 6 feet away from the wall, how far up the wall does the ladder reach?
8 feet
Define Pythagorean theorem.
It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
A right triangle has one leg measuring 8 centimeters and the hypotenuse measuring 10 centimeters. What is the length of the other leg?
Answer: Using the Pythagorean theorem: C = V102 - 82 = 100 - 64 = V36 = 6
centimeters.
Problem 3:
If the length of one leg of a right triangle is 15 inches and the length of the hypotenuse is 17 inches, what the length of the other leg
Answer: Using the Pythagorean theorem: a = V262 - 102 = V676 - 100 = V576 = 24
meters.
A baseball diamond is a square with sides of 90 feet. How far is it from home plate to second base
127.28 feet
Question: What are the two shorter sides of a right triangle called?
Legs
If the lengths of the legs of a right triangle are 6 inches and 8 inches, what is the length of the hypotenuse?
Answer: Using the Pythagorean theorem: c = /62 + 82 = V36 + 64 = V100 = 10
inches.
In a right triangle, if one leg measures 9 feet and the hypotenuse measures 15 feet, what is the length of the other leg
Using the Pythagorean theorem: a = V152 - 92 = V225 - 81 = V144 = 12
feet.
A flagpole casts a shadow that is 15 feet long. If the angle of elevation from the tip of the shadow to the top of the flagpole is 30 degrees, how tall is the flagpole
30feet
: In the Pythagorean theorem a + 6? = c', what do 'a', 'b', and 'c'
represent?
'a' and 'b' represent the lengths of the legs of the right triangle, while 'c'
In a right triangle, one leg measures 15 meters and the hypotenuse measures 17 meters. What is the length of the other leg?
Answer: Using the Pythagorean theorem: c = V172 - 152 = V289 - 225 = V64 = 8
meters.
A right triangle has one leg measuring 8 centimeters and the hypotenuse measuring 10 centimeters. What is the length of the other leg
Using the Pythagorean theorem: a = V102 - 82 = V100 - 64 = 136 = 6
If the lengths of the legs of a right triangle are 3 and 4 units, what is the length of the hypotenuse according to the Pythagorean theorem?
c = V32 + 42 = V9 + 16 = V25 = 5 units.