a flagpole cast a shadow 18m long when the altitude of the sun is 54 degrees.what is the height of the flagpole
Well, let me "pole" you in the right direction! Given that the shadow cast by the flagpole is 18m long and the altitude of the sun is 54 degrees, we can use a little trigonometry to figure out the height of the flagpole.
We can use the tangent function, which is the ratio of the opposite side (height of the flagpole) to the adjacent side (length of the shadow).
So, tan(54 degrees) = height of the flagpole / 18m.
To solve for the height of the flagpole, we'll multiply both sides by 18m:
Height of the flagpole = 18m * tan(54 degrees).
Now, let me grab my handy-dandy calculator, and I'll give you the answer. *Calculating sounds*
Voila! The height of the flagpole is approximately [insert answer here]. Just remember, I'm a Clown Bot, not a math whiz, so double-check your calculations to be on the safe side!
To determine the height of the flagpole, we can use the basic trigonometric function tangent. The tangent function relates the angle of elevation (or depression) to the opposite and adjacent sides of a right triangle.
In this scenario, the flagpole is the height we're trying to find, and the shadow it casts is the adjacent side of the triangle. The angle of elevation is given as 54 degrees.
Using the tangent function, we can set up the equation:
tan(54 degrees) = height of the flagpole / 18m
To solve for the height of the flagpole, we need to isolate it. Multiplying both sides by 18m gives us:
18m * tan(54 degrees) = height of the flagpole
Now, we can calculate the height of the flagpole using a calculator:
Height of the flagpole = 18m * tan(54 degrees)
Calculating this equation gives us:
Height of the flagpole ≈ 18m * 1.37638
Height of the flagpole ≈ 24.775 m
Therefore, the height of the flagpole is approximately 24.775 meters.
To find the height of the flagpole, we can use trigonometry. We know that the shadow cast by the flagpole is 18 meters long, and the altitude of the sun is 54 degrees. We can define the height of the flagpole as the opposite side (h) and the shadow as the adjacent side (18m). The angle between the ground and the sun's rays is the reference angle.
The trigonometric function that relates the opposite side and the adjacent side to the angle is the tangent function:
tan(angle) = opposite / adjacent
In this case, we want to find the opposite side (h), so we can rearrange the formula:
h = tan(angle) * adjacent
Now we can substitute the given values:
h = tan(54°) * 18m
Using a calculator, we can find the tangent of 54 degrees:
tan(54°) ≈ 1.376381920471173
Now we can calculate the height of the flagpole:
h ≈ 1.376381920471173 * 18m
h ≈ 24.77487457048011m
Therefore, the height of the flagpole is approximately 24.77 meters.
h/18 = tan 54
now it's clear what h is.