A building 200 feet tall casts an 80 ft long shadow. If a person looks down from the top of the building which of the following is the measure of the angle between the end of the shadow and the vertical side of the building to the nearest degree? I understand that you would have to solve for Tan since your givens are 200 (Opposite) and 40 (Adjacent) so your Tan would be 2.5 but I'm confused as to what I should do next? Can someone help me and list all the steps out?
it's 22°
Sure, I'd be happy to help you with this problem.
To find the measure of the angle between the end of the shadow and the vertical side of the building, you can use the inverse tangent function (arctan).
Let's call the angle we want to find "x".
You correctly identified the sides of the right triangle formed by the building, its shadow, and the line connecting the top of the building and the end of the shadow:
- Opposite side (from the top of the building to the end of the shadow) = 200 ft
- Adjacent side (from the top of the building to the base) = 80 ft
To find x, you can use the formula for tangent: tan(x) = opposite/adjacent. Since you want to find x, you can rearrange the equation: x = arctan(opposite/adjacent).
Now, let's substitute the given values into the formula and calculate:
x = arctan(200/80)
x = arctan(2.5)
Using a calculator, you can find the arctan of 2.5 to be approximately 68.2 degrees.
Therefore, the measure of the angle between the end of the shadow and the vertical side of the building is approximately 68 degrees to the nearest degree.
I hope this helps! If you have any more questions, feel free to ask!
Sure! I can help you with that. To find the measure of the angle between the end of the shadow and the vertical side of the building, you can use the inverse tangent function. Here are the steps:
1. Write down the given information:
- Opposite side (vertical side of the building): 200 ft
- Adjacent side (length of the shadow): 80 ft
2. Calculate the tangent of the angle:
- Tangent (tan) = Opposite / Adjacent = 200 / 80 = 2.5
3. Use the inverse tangent (arctan) function to find the angle:
- Angle = arctan(tan) = arctan(2.5)
4. Use a calculator to find the arctan (inverse tangent) of 2.5. The result will be the measure of the angle in degrees.
Hope this helps! Let me know if you have any further questions.
Sure! I can help you with that. To find the measure of the angle between the end of the shadow and the vertical side of the building, we need to use the trigonometric function "arctan" (also known as the inverse tangent). Here are the steps:
1. First, identify the given sides of the right triangle formed by the building, its shadow, and the vertical side.
- Opposite side: The height of the building, which is 200 feet.
- Adjacent side: The length of the shadow, which is 80 feet.
2. Next, calculate the value of the tangent of the angle using the ratio of the opposite side to the adjacent side: tan(θ) = opposite/adjacent.
In this case, tan(θ) = 200/80 = 2.5.
3. Now, we need to find the angle itself by using the inverse tangent (or arctan) function.
Take the arctan of both sides of the equation: θ = arctan(tan(θ)) = arctan(2.5).
4. Use a calculator that has the arctan function to find the value of arctan(2.5).
The answer will be the angle θ in radians.
5. Finally, convert the angle from radians to degrees.
Multiply the angle in radians by 180/π to get the measure of the angle in degrees.
So, following these steps, you should be able to find the measure of the angle between the end of the shadow and the vertical side of the building to the nearest degree.
you are correct so far. Of course, you have not provided any choices for selection, but the equation you need is
tanθ = 200/80
θ = tan-1 2.5 ≈ 68°