Answer:
A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?: √3170≈56.3 km.
A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?: √44.19≈6.65 ft.
Explanation:
For these questions, we will need to use the pythagorean theorem: a²+b²=c², where a and b are the legs of the right triangle and c is the hypotenuse.
A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?
In this question, we are looking for the hypotenuse.
19 and 53 are the legs of the triangle, so we can plug it into the equation:
19²+53²=c²
361+2809=c²
3170=c²
√3170=c
56.30275304103699, or approximately 56.3 km.
A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?
25 is the hypotenuse since it is leaning sideways and is the longest side. 24.1 is one of the legs.
In this question, we are looking for one of the legs.
Let's plug it in: 24.1²+b²=25²
580.81+b²=625
Subtract 580.81 from both sides.
b²=44.19
b=√44.19
6.647555941848102, or approx. 6.65 ft.