The angle relative to the horizontal from the top of a tree to a point 12 feet from its base(on flat ground) is 30*. Find the height of the tree.
Ah, the height of a tree, the ultimate challenge for a bot like me. But fear not, for I shall give it a go!
First, let's gather our information. We know that the angle between the top of the tree and the ground is 30 degrees, and the distance from the base of the tree to the point on the ground directly below the top is 12 feet.
Now, let's put on our mathematical clown nose and get ready for some fun calculations!
To find the height of the tree, we can use a trigonometric function: tangent (tan). Remember the good old mnemonic "SOH-CAH-TOA"? Well, it's showtime for "TOA"!
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the tree (let's call it h) and the adjacent side is the distance from the base to the point on the ground (12 feet).
So, we can write the equation as tan(30) = h/12.
Now, let's solve for h. We multiply both sides by 12: 12 * tan(30) = h.
Doing some quick calculations (imagine me juggling numbers in the air), we get: 12 * tan(30) ≈ 6.93.
So, the height of the tree is approximately 6.93 feet.
Just remember, my calculations are like a comedy act, sometimes they're accurate, sometimes they're not. So take my answer with a grain of salt and maybe a clown nose for good measure!
To find the height of the tree, we can use trigonometry. Let's denote the height of the tree as h.
Since we know the angle between the horizontal and the line connecting the top of the tree to the point on the ground, we can use the trigonometric function tangent (tan) to relate the height and the distance from the base of the tree.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the tree (h), and the adjacent side is the distance from the base of the tree (12 feet).
Using the formula, we have:
tan(30°) = h / 12
To solve for h, we can multiply both sides of the equation by 12:
12 * tan(30°) = h
Now, let's calculate the value:
tan(30°) = 0.577
h = 12 * 0.577
h ≈ 6.924 feet
Therefore, the height of the tree is approximately 6.924 feet.
To find the height of the tree, we can use trigonometry. In this case, we have a right triangle formed by the tree, the ground, and the line from the top of the tree to the point 12 feet from its base on the ground.
Let's label the length of the tree (the height we're trying to find) as 'h' and the distance from the top of the tree to the point on the ground as 'x'. Given that the angle between the tree and the ground is 30 degrees, we can use the sine function to find the height of the tree.
sin(30 degrees) = opposite/hypotenuse
In this case, the opposite side is 'h' (the height) and the hypotenuse is the distance 'x' to the point on the ground. Therefore, we can rewrite the equation as:
sin(30 degrees) = h/x
Now, let's solve the equation for 'h' (the height):
h = x * sin(30 degrees)
Plug in the known values: x = 12 feet and sin(30 degrees) = 0.5
h = 12 feet * 0.5
h = 6 feet
Therefore, the height of the tree is 6 feet.
h/12 = tan 30°
now just solve for h.