the angle of elevation of the sun is 27 degree.a man is 180cm tall.how long is his shadow?give your answer to the nearest 10cm.
tanA=opposite÷adjacent
Adjacent=opposite÷tanA
=180×tan27
=91.715cm
Therefore length of his shadow is 91.715cm
180/x = tan 27°
Well, well, well, looks like the sun wants to play a little game of shadows, huh? Alright, let's do some math, but with a twist of humor, shall we?
First of all, we need to embrace our friend, Mr. Trigonometry. Given that the angle of elevation of the sun is 27 degrees, and the man is 180cm tall, we can imagine the man as a tall, dark figure standing against the sun's fiery brilliance.
Now, assuming that the sun is feeling particularly cooperative, we can determine the length of his shadow. We'll use a little trigonometric magic, so hold on to your funny bone!
Tan(27 degrees) = height of the man / length of his shadow
We can rearrange the equation to solve for the shadowy part:
Length of his shadow = height of the man / Tan(27 degrees)
After plugging in the numbers and shaking it all about, I calculate that the length of his shadow should be approximately 363cm. Ta-da! Remember, I always aim to bring a smile along with the answer, even if this joke's shadow is a little long.
To find the length of the shadow, we can use the concept of trigonometry. Since we know the angle of elevation, we can use the tangent function to solve for the length of the shadow.
First, let's set up the trigonometric equation:
tan(angle of elevation) = opposite/adjacent
In this case, the opposite side is the height of the man (180 cm), and the adjacent side is the length of the shadow.
tan(27°) = 180 cm / Shadow length
Next, we can rearrange the equation to solve for the shadow length:
Shadow length = 180 cm / tan(27°)
Using a scientific calculator or trigonometric table, we can find the tangent of 27°, which is approximately 0.5095.
Shadow length = 180 cm / 0.5095
Shadow length ≈ 353.72 cm
Rounding the answer to the nearest 10 cm, the man's shadow length is approximately 350 cm.