WEBVTT
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A rocket is launched vertically upward.
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A woman, standing four miles from the launchpad, watches its flight.
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What is the angle of elevation of the rocket from the women when its altitude is 11 miles?
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Letโs begin by sketching a diagram of this scenario.
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Remember, a sketch does not need to be to scale.
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But it should be roughly in proportion so we can check the suitability of any answers we get.
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Letโs call the woman ๐ด and the launchpad ๐ต.
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The distance between ๐ด and ๐ต is four miles.
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The rocket launches vertically upwards, which means that the angle between the trajectory of the rocket and the ground is 90 degrees.
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Weโre interested in the moment that the rocket โ letโs call that ๐ถ โ is at an altitude of 11 miles.
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So the length ๐ต๐ถ is 11 miles.
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We are looking to find the angle of elevation of the rocket from the woman.
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Itโs the angle between the horizontal and the line from the rocket to the womanโs eye.
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Thatโs angle ๐ถ๐ด๐ต, which weโve called ๐.
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So we have a right-angled triangle with two known lengths, in which weโre trying to find a missing angle.
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Weโll need to use right-angle trigonometry to do this.
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We can start by labelling the triangle.
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The hypotenuse is the longest side.
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Itโs the side situated directly opposite the right angle.
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The opposite side is the side opposite the given angle.
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Itโs the one furthest away from the angle ๐.
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Finally, the adjacent side is the other side.
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Itโs located next to the angle ๐.
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We know both lengths of the opposite and the adjacent sides.
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This means we need to use the tangent ratio.
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Tan of ๐ is equal to opposite over adjacent.
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The length of the opposite side of our triangle is 11 miles, and the length of the adjacent side is four.
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So our equation becomes tan ๐ is equal to 11 over four.
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To solve this equation for ๐, we want to find the inverse tan of both sides.
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The inverse tan of tan of ๐ is simply ๐.
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So our equation becomes ๐ is equal to the inverse tan of 11 over four.
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If we type inverse tan of 11 over four into our calculator, we get 70.016, and so on.
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Correct to two decimal places, the angle of elevation of the rocket from the woman is 70.02 degrees.