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a plane takes off at an angle of elevation of 15 degrees and travels in

a plane takes off at an angle of elevation of 15 degrees and travels in a straight line for 3,000 meters. What is the height of the plane above the ground at this instant?

2 months ago

Solution 1

Guest Guest #2199
2 months ago
SOH CAH TOA tells you the sine function of an angle gives the ratio of opposite side to the hypotenuse of the right triangle.
  Sin = Opposite/Hypotenuse
In this problem, the angle is 15°, the hypotenuse is 3000 m and we want to find the length of the opposite side (the height above the ground).

  sin(30°) = height/(3000 m)
Multiplying by 3000 m, we get
  height = (3000 m)*sin(30°) = 1500 m

The height of the plane at that instant is ...
  1500 m

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Solution 2
Well, is namely just their sum, let's firstly convert the mixed fractions to "improper" and then add them,

\bf \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}}
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\stackrel{mixed}{9\frac{3}{4}}\implies \cfrac{9\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{39}{4}}\\\\
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\cfrac{23}{3}+\cfrac{39}{4}\qquad \stackrel{LCD~of~12}{\implies }\qquad \cfrac{4(23)+3(39)}{12}\implies \cfrac{92+117}{12}
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