Russell Grossman is training for the Olympics. He wants to know the distance across lake royal, so he can write in his training logbook how far he rows each day. If from one point on the shore to one side of the lake is 13 km and from the same point to another side of the lake is 16km, what is the approximate length in km of the lake?
9
18***
44
87
erika is flying a kite. if the length of string is 125 meters and the distance between where erika is standing to the vertical distance from the kite is 75 meters, how high is the kite in meters?
125
100***
25
15
a lader is leaning against a house. the distance between the base of the ladder to the house is 3 feet. the length of the ladder is 10 feet. in feet, how far above the ground does the ladder touch the house?
4.2
9.5***
10.4
14.1
a wire is streched from the top of a 26 foot pole to a point on the ground that is 15 feet from the bottom of the pole. approximately how long is the wire in feet?
16
21
30****
37
robin hikes due south for 6 km. then she hikes due east for 3.25km. what is the best estimate, in km, of the distance from her starting point?
7****
8
9
10
can you check them?
They are correct! Great Job! :)
all of them
your wrong the first one is 9
To find the distance across Lake Royal, we can use the concept of Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse (the longest side).
In this scenario, the two shorter sides of the triangle are the distances from one point on the shore to each side of the lake, which are 13 km and 16 km. Let's call the length of the lake (the hypotenuse) "x."
Using the Pythagorean theorem, we can set up an equation:
13^2 + 16^2 = x^2
Simplifying this equation:
169 + 256 = x^2
425 = x^2
To find the value of x, we can take the square root of both sides of the equation:
√425 ≈ 20.62
Therefore, the approximate length of Lake Royal is 20.62 km.