Alfonso knows that the distance across the field from his home to Carla's home is 50 meters. A nice place to pick flowers is 40 meters directly east of his home and directly south of Carla's home. How far from Carla's home is the flower-picking spot?
You've described a right angle triangle. The hypotenuse is 50 meters. One leg of the triangle is 40 meters. The other leg (the distance from Carla's home to the flowers) is the other leg.
In this equation, c = 50 and a = 40. Solve for b using this formula:
a^2 + b^2 = c^2.
If you post your answer, we'll be glad to check it.
a^2. does that mean squared??
Yes. a^2 means a squared.
(40)^2 + b^2 = (50)^2
1600 + b^2 = 2500
-1600 -1600
b^2 = 900
im not sure wat the next step is
You're right so far. :-)
The next step is to take the square root of 900. That will tell you the distance from Carla's house to the flowers.
ok i see.i was'nt sure what the opposite of b^2 would be.
thesquare root of 900 is 30.
the distance from Carla's house to the flowers is 30 meters.
You're right! Yay!
90
To find the distance from Carla's home to the flower-picking spot, we can use the Pythagorean theorem, which says that in a right-angled 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.
In this scenario, the distance from Alfonso's home to Carla's home is the base of the right-angled triangle, measuring 50 meters. The flower-picking spot is 40 meters directly east of Alfonso's home and 40 meters directly south of Carla's home, forming the other two sides of the triangle.
Let's denote the distance from Carla's home to the flower-picking spot as "d". We can then set up our equation using the Pythagorean theorem:
d² = (50²) + (40²)
d² = 2500 + 1600
d² = 4100
To solve for "d", we take the square root of both sides:
d = √4100
d ≈ 64.03 meters
Therefore, the flower-picking spot is approximately 64.03 meters from Carla's home.