Two girls are playing with a ball in the yard when the ball got stuck in the tree. It's too high for them to reach, so they get a ladder. when the 13ft ladder is leaned against the tree, the top of the ladder is even with the ball. the distance between the base of the tree and the bottom of the ladder is 5 ft. how high is the ball in the tree?
answers
a. The hypotenuse is 13 feet & looking for side c. (distance between ladder & tree)
b. the hypotenuse is 5 feet and we are looking for side b (height of ball in tree)
c. The hypotenuse is 13 feet and we are looking for side b. (height of ball in tree) **
To find the length of the short cut, we can use the Pythagorean theorem.
Let's call the length of the lot A and the width of the lot B.
A = 120 feet
B = 50 feet
We can use the Pythagorean theorem to find the length of the short cut (C).
The formula is:
C^2 = A^2 + B^2
Substituting the given values:
C^2 = 120^2 + 50^2
C^2 = 14400 + 2500
C^2 = 16900
Taking the square root of both sides, we find:
C = √16900
C ≈ 130 feet
Therefore, the length of the short cut is approximately 130 feet.
c. The hypotenuse is 13 feet and we are looking for side b. (height of ball in tree) **
What formula can we use to find how high the ball is in the tree?
We can use the Pythagorean theorem to find how high the ball is in the tree. The formula is:
c^2 = a^2 + b^2
where c is the hypotenuse (13 feet in this case), and a and b are the other two sides of the triangle. In this case, we want to find side b, so the formula becomes:
b^2 = c^2 - a^2
Substituting the given values:
b^2 = 13^2 - 5^2
Now we can solve for b.
Would B= 12 feet or 14 feet?
To find the value of b, we can substitute the given values into the equation:
b^2 = 13^2 - 5^2
b^2 = 169 - 25
b^2 = 144
Taking the square root of both sides, we find:
b = √144
b = 12 feet
Therefore, the height of the ball in the tree is 12 feet.
Jaya starts driving north for 9 miles, then takes a right turn, and then he drives east for another 40 miles. at the end of driving, what is the distance of a straight line from the starting point?
To find the distance of a straight line from the starting point, we can use the Pythagorean theorem.
Let's call the northward distance A and the eastward distance B.
A = 9 miles (north)
B = 40 miles (east)
We can use the Pythagorean theorem to find the distance of the straight line from the starting point (C).
The formula is:
C^2 = A^2 + B^2
Substituting the given values:
C^2 = 9^2 + 40^2
C^2 = 81 + 1600
C^2 = 1681
Taking the square root of both sides, we find:
C = √1681
C ≈ 40.99 miles
Therefore, the distance of the straight line from the starting point is approximately 40.99 miles.