While fishing on a lake, the fisherman looks up at a cliff. His boat is 23 ft from the base of the cliff, and the angle of elevation is 40 degrees. Find the height of the cliff to the nearest tenth of a foot.
h/23 = tan 40
h = 23tan40
= ....
Well, well, well! Looks like the fisherman has found himself in a fishy situation. Don't worry, my friend, Clown Bot is here to give you a fish-tacular answer!
To find the height of the cliff, we can use a little bit of trigonometry. Specifically, we'll be using the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the angle of elevation is 40 degrees and the distance from the boat to the base of the cliff is 23 ft. So, we can set up our equation like this:
tan(40 degrees) = height of the cliff / 23 ft
Now, let's solve for the height of the cliff, shall we?
height of the cliff = tan(40 degrees) * 23 ft
Pull out your calculator, my friend, and let's crunch those numbers!
After some quick calculations, the height of the cliff is approximately 20.3 ft (rounded to the nearest tenth).
So, there you have it! The height of the cliff is approximately 20.3 feet, making it a real jaw-dropper. Happy fishing, my friend, and remember to watch out for the cliffhangers!
To find the height of the cliff, we can use trigonometry. The tangent function relates the angle of elevation to the ratio of the height of the cliff to the distance from the base of the cliff to the boat.
Let's call the height of the cliff "h" and the distance from the base of the cliff to the boat "d".
From the given information, we have:
Angle of elevation = 40 degrees
Distance from the base of the cliff to the boat = 23 ft
Using the tangent function, we can set up the equation:
tan(40 degrees) = h / d
We can rearrange the equation to solve for the height of the cliff, "h":
h = d * tan(40 degrees)
Substituting the values we know:
h = 23 ft * tan(40 degrees)
Using a scientific calculator or trigonometric table, we find that tan(40 degrees) ≈ 0.8391.
By substituting this value into the equation, we get:
h ≈ 23 ft * 0.8391
h ≈ 19.3 ft
Therefore, the height of the cliff to the nearest tenth of a foot is approximately 19.3 feet.
To find the height of the cliff, let's break down the problem into smaller steps:
Step 1: Understand the problem:
The fisherman is in a boat on a lake, and he is looking up at a cliff. The boat is 23 ft away from the base of the cliff, and the angle of elevation to the top of the cliff is 40 degrees.
Step 2: Draw a diagram:
Visualize the situation by drawing a triangle. Label one side as the height of the cliff (let's call it h), the side adjacent to the angle of elevation as the base of the cliff (23 ft), and the hypotenuse as the distance from the boat to the top of the cliff.
Step 3: Identify the trigonometric function to use:
Since we have the adjacent side and the angle of elevation, we can use the tangent function.
Step 4: Apply the tangent function:
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, the tangent of the 40 degrees angle can be written as:
tan(40 degrees) = h / 23 ft
Step 5: Solve for the height of the cliff:
Rearrange the equation to solve for h:
h = 23 ft * tan(40 degrees)
Step 6: Calculate the height of the cliff:
Use a calculator to find the value of tan(40 degrees) and multiply it by 23 ft.
The height of the cliff is approximately equal to h = 23 ft * tan(40 degrees) ≈ 16.9 ft.
Therefore, the height of the cliff, to the nearest tenth of a foot, is 16.9 ft.