Tutor profile: Jay M.
Jack was standing 322 ft from his toy drone when it took off perpendicular to the horizon. After 5 seconds Jack had to look up 51 degrees from the horizon to see his drone. Rounding to the nearest hundredth, how high was his drone after 5 seconds? (NOTE: Jack's eyes are 5'4" off of the ground)
Utilizing the given data we know that the angle of elevation created a right triangle whose adjacent side is represented by the 322' and whose opposite side is represented by h (the height of the drone after 5 seconds). Utilizing Trigonometric ratios we see that we will be solving for the opposite side utilizing the tangent function (ensure your calculate is set to degrees and not radians). tan 55 = h/322 (tan 55)322 = h 459.86' = h For the final step we need to add the distance from Jack's eyes to the horizon. 5'4" = 5.333...' 459.86 + 5.33333... = 465.19' off of the ground
Jack is trying to make a triangular flower garden in corner of his back yard where his fence connects to his house. Jack is hoping to use some scrap 2x4's he already owns without having to cut any of them. If they measure 3'2", 4'2", and 5', will Jack be able to make this flower garden without making any cuts? (NOTE: assume the corner of the house and the fence make a right angle)
Of the fence and the house make a right angle where they connect - then the triangle made in this corner will be a right triangle. Therefore these three sides should prove true in Pythagorean's Theorem with 5' representing the hypotenuse and 3'2" and 4'2" representing the legs of the right triangle. Let's plug these measurements into Pythagorean's Theorem and see if it works! (NOTE: we will need to convert everything to one unit of measure to do this. so 3'2" = 38"; 4'2" = 50"; and 5' = 60") a^2 + b^2 = c^2 38^2 + 50^2 = 60^2 3944 = 3600 Obviously 3944≠3600, so these three 2x4's could not be a right triangle unless Jack cut the sides.
It took Jack 5 years to get his first raise at work. After that first year his employer began giving Jack a $0.50 per hour every year. If Jack started his job making $19.25 per hour, how much will he be making after 13 years?
Since Jack did not get a raise until year 5, we know that he received 13-5=7 years worth of raises. If he received $0.50 per hour raise every year, we can find his how much his pay rate has increased by the following formula: p=.50t + 19.25 where p stands for how much he is making after t years on the job. To find out how much he is making at year 13 we would substitute 7 for t (because he didn't begin to get a raise until year 5) and solve for p. p=.50(7) + 19.25 p=3.50 + 19.25 p=22.75 Jack would be making $22.75 per hour after 13 years on the job.
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