Two questions?
Build a patio-hypotenuese is 50 feet long
the two sides of patio are same. What is the length of one side of the patio
I think I set it up a^2 + b^2 = c^2
a^2 + b^2 = 50^2
a^2+ b^2 = 2500
then I just could say 2a^2 = 2500
a^2 = 2500/2
a^2 = 1250
sqrt of 1250 = 35.36 correct?
2nd question? Boat across a river with the current moving you downstream so the boat goes at a 30 degree angle. If the river is 400 feet across, how far downstream do you end up-this one I'm totally confused on
first question is correct.
2nd:
The way I read your question ....
drew a line straight across, called it 400 ft
then from starting point drew a line 30° from the 400 line.
got a right-angled triangle, called the distance downstream x ft
tan 30° = x/400
x = 400 tan 30°230.94
I'm not sure I'm understanding the x=
400 tan 30 *230.94 or would it be that it equals 230.94
that's a typo
should have been
x = 400 tan 30°
= 230.94
For the first question, you set up the Pythagorean theorem correctly to find the length of one side of the patio. Let's go through the solution step by step.
Given:
Hypotenuse (c) = 50 feet
Length of the two sides of the patio (a = b)
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the given values:
a^2 + b^2 = 50^2
a^2 + b^2 = 2500
Since the two sides of the patio are the same (a = b), we can rewrite the equation as:
2a^2 = 2500
Dividing both sides by 2:
a^2 = 1250
To find the length of one side (a), we take the square root of both sides:
√(a^2) = √1250
a ≈ 35.36
So, the length of one side of the patio is approximately 35.36 feet.
Now, let's move on to the second question about the boat crossing the river.
Given:
Distance across the river (width) = 400 feet
Angle with the current = 30 degrees
To find how far downstream the boat ends up, we'll need trigonometry and the concept of vector addition.
First, we need to break down the boat's velocity into horizontal and vertical components. The velocity with the current provides the horizontal component, and the velocity perpendicular to the current provides the vertical component.
The horizontal component (downstream velocity) is determined by the current, and the vertical component (cross-river velocity) is determined by the boat's own speed relative to the water.
Using trigonometry, we can find the horizontal component (downstream velocity):
downstream velocity = velocity with current * cos(angle)
Given that the angle is 30 degrees and the width of the river is 400 feet, we can substitute these values into the formula:
downstream velocity = velocity with current * cos(30)
The horizontal distance traveled downstream is based on the time taken to cross the river, which is equal to the width divided by the downstream velocity:
distance downstream = width / downstream velocity
Now, calculate the downstream velocity:
downstream velocity = velocity with current * cos(30) = 400 * cos(30) ≈ 346.41 feet
Finally, calculate the distance traveled downstream:
distance downstream = width / downstream velocity = 400 / 346.41 ≈ 1.153 feet
Therefore, the boat ends up approximately 1.153 feet downstream.