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Answer :
To solve this problem, we need to find the height of the rocket above the ground level based on the given information. Here's a step-by-step solution for this:
1. Identify the Given Information:
- The observer is [tex]\( x \)[/tex] meters away from the base of the launch pad.
- The rocket is seen at an angle of [tex]\( q \)[/tex] degrees from the horizontal.
2. Understand the Trigonometric Relationship:
- We can use the tangent of the angle [tex]\( q \)[/tex] in right-triangle trigonometry, which relates the opposite side (height of the rocket) to the adjacent side (distance [tex]\( x \)[/tex]).
The tangent function is defined as:
[tex]\[
\tan(q) = \frac{\text{opposite side}}{\text{adjacent side}}
\][/tex]
Here, the opposite side is the height of the rocket above the ground, and the adjacent side is the distance [tex]\( x \)[/tex].
3. Set Up the Equation:
[tex]\[
\tan(q) = \frac{\text{height}}{x}
\][/tex]
Solving for the height, we get:
[tex]\[
\text{height} = x \cdot \tan(q)
\][/tex]
4. Determine the Correct Answer:
- The height of the rocket above the ground is given by [tex]\( x \cdot \tan(q) \)[/tex].
By comparing this with the provided answer choices, we can see that the correct option is:
[tex]\[ \boxed{x \tan 9} \][/tex]
So, the height of the rocket above the ground at that instant is [tex]\( x \tan q \)[/tex] meters.
1. Identify the Given Information:
- The observer is [tex]\( x \)[/tex] meters away from the base of the launch pad.
- The rocket is seen at an angle of [tex]\( q \)[/tex] degrees from the horizontal.
2. Understand the Trigonometric Relationship:
- We can use the tangent of the angle [tex]\( q \)[/tex] in right-triangle trigonometry, which relates the opposite side (height of the rocket) to the adjacent side (distance [tex]\( x \)[/tex]).
The tangent function is defined as:
[tex]\[
\tan(q) = \frac{\text{opposite side}}{\text{adjacent side}}
\][/tex]
Here, the opposite side is the height of the rocket above the ground, and the adjacent side is the distance [tex]\( x \)[/tex].
3. Set Up the Equation:
[tex]\[
\tan(q) = \frac{\text{height}}{x}
\][/tex]
Solving for the height, we get:
[tex]\[
\text{height} = x \cdot \tan(q)
\][/tex]
4. Determine the Correct Answer:
- The height of the rocket above the ground is given by [tex]\( x \cdot \tan(q) \)[/tex].
By comparing this with the provided answer choices, we can see that the correct option is:
[tex]\[ \boxed{x \tan 9} \][/tex]
So, the height of the rocket above the ground at that instant is [tex]\( x \tan q \)[/tex] meters.
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Rewritten by : Barada
