A boat is 15 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 65° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work.
Well, this seems like quite the geometry problem! I'll give it a shot.
Let's call the distance from the person to the closest point to the boat "x". And let's call the distance from the closest point to the boat to the boat itself "y".
We have a triangle formed with two sides of length x and y, and an angle of 65° between them. We want to find x.
To do this, we can use the sine function: sin(65°) = x/y
Rearranging the equation, we get x = y * sin(65°)
Now, we know that the boat is 15 ft away from the closest point to the shore, which means that y = 15 ft.
Plugging in the values, we get x = 15 ft * sin(65°)
Calculating that, we find that x ≈ 13.4 ft.
So, the person is approximately 13.4 ft away from the boat.
Now, let me tell you a joke to lighten the mood! Why don't scientists trust atoms? Because they make up everything!
To solve this problem, we can use trigonometry.
Let's call the distance between the person and the boat x feet.
We are given that the boat is 15 feet away from a point perpendicular to the shoreline, so the boat forms a right angle with this perpendicular line.
We are also given that a 65° angle is formed between the closest point to the boat, the person, and the boat.
Using trigonometry, we can set up the equation:
tan(65°) = x / 15
Now we can solve for x:
x = 15 * tan(65°)
Using a calculator, we find that tan(65°) ≈ 2.1445
Substituting this value back into the equation:
x = 15 * 2.1445 ≈ 32.1675
Therefore, the person is approximately 32.2 feet away from the boat.
To solve this problem, we can use trigonometry, specifically the tangent function. Here's how we can approach this:
Let's call the distance from the person to the boat "x". We are given that the boat is 15 ft away from a point perpendicular to the shoreline, which means the distance from the boat to the closest point on the shoreline is also 15 ft.
Now, in the right triangle formed by the person, the closest point to the boat, and the boat itself, the angle between the closest point, the person, and the boat is 65°.
We can use the tangent function to find the value of x. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In our case, the side opposite the angle of 65° is x, and the side adjacent is 15 ft. So, we have:
tan(65°) = x / 15
Using a scientific calculator, let's find the value of tan(65°):
tan(65°) ≈ 2.1445069
Now, we can solve for x by multiplying both sides of the equation by 15:
2.1445069 = x / 15
x = 2.1445069 * 15
x ≈ 32.1686043
Rounding to the nearest tenth of a foot, the person is approximately 32.2 ft away from the boat.
Draw the diagram and review your basic trig functions. It should be clear that the distance x can be found using
15/x = sin65°
x = 16.55 ft