Math Trig Problem

Updated: 6/3/2020

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- Help! My name's Tom, and I'm being chased by a bad guy! The only escape I have is to jump the fence- but I don't know if I can do it!
- Note: x is drawn to be the hypotenuse of a right triangle, where side a is the distance from Tom to the gate, side b is the height of the gate.
- I can only jump about 10 feet forward, so I'm going to find if x <= 15. But how can I do that?
- x
- First, I know I'm standing about 8 feet from the gate. I can also measure the height of the gate!
- 8 feet
- So I can't measure the gate because I don't have a tape measure, but I do have a protractor! I know that i would be jumping at a 40º angle, because it has to be long enough to make it over, and too high. This means that the angle from the reverse slant is 50º, because a triangle has 180 degrees total. Here's a visual.
- X
- 8 feet
- 40º
- 50º
- Now we solve for X. I can calculate the cosine of 40º to find the hypotenuse by solving for this equation:Cos(40º)= 8/XWhere 8 is the adjacent side, and X is the hypotenuse. I used my handy calculator on my phone, and the cos(40º)= 0.77. Now we can solve by cross-multiplying:0.77 • X= 88/0.77= 10.4 feet
- Phew! What a relief to know I should just be able to escape! Thanks for your help! Adios, amigos!