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Answer :
To find the angle separating Aaron and Jason from Aaron's viewpoint, given that they are 900 feet apart horizontally and Jason is 30 feet below Aaron, we can use some basic trigonometry. Here's how we do it:
1. Identify the right triangle: In this scenario, we're looking at a right triangle where:
- The horizontal distance between Aaron and Jason is the base of the triangle and measures 900 feet.
- The vertical distance between them, which is how far below Jason is from Aaron, is the height of the triangle and measures 30 feet.
2. Understand the trigonometric function involved: To find the angle between them from Aaron's viewpoint, we use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (vertical distance) to the adjacent side (horizontal distance).
3. Calculate the angle using tangent:
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{30}{900}
\][/tex]
4. Find the angle in radians: Use the inverse tangent function (often denoted as arctan or atan) to find the angle in radians.
- [tex]\(\theta = \arctan\left(\frac{30}{900}\right)\)[/tex].
5. Convert radians to degrees: Angles can be expressed in degrees or radians. To convert the angle from radians to degrees, use the conversion [tex]\(180^\circ/\pi\)[/tex].
6. Round the answer: Finally, we round the angle to one decimal place.
Following these calculations, we arrive at an angle of approximately 1.9 degrees. This means the angle between Aaron and Jason, from Aaron's viewpoint, is 1.9°.
1. Identify the right triangle: In this scenario, we're looking at a right triangle where:
- The horizontal distance between Aaron and Jason is the base of the triangle and measures 900 feet.
- The vertical distance between them, which is how far below Jason is from Aaron, is the height of the triangle and measures 30 feet.
2. Understand the trigonometric function involved: To find the angle between them from Aaron's viewpoint, we use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (vertical distance) to the adjacent side (horizontal distance).
3. Calculate the angle using tangent:
[tex]\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{30}{900}
\][/tex]
4. Find the angle in radians: Use the inverse tangent function (often denoted as arctan or atan) to find the angle in radians.
- [tex]\(\theta = \arctan\left(\frac{30}{900}\right)\)[/tex].
5. Convert radians to degrees: Angles can be expressed in degrees or radians. To convert the angle from radians to degrees, use the conversion [tex]\(180^\circ/\pi\)[/tex].
6. Round the answer: Finally, we round the angle to one decimal place.
Following these calculations, we arrive at an angle of approximately 1.9 degrees. This means the angle between Aaron and Jason, from Aaron's viewpoint, is 1.9°.
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