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## Geometry (all content)

### Course: Geometry (all content)>Unit 13

Lesson 5: Modeling with right triangles

# Right triangle word problem

Sal solves a modeling problem where he finds the necessary angle to shoot at a vicious alien. Created by Sal Khan.

## Want to join the conversation?

• Could someone explain again what is the difference between tan and tan-1? Why did Sal use tan-1 instead of tan?
• hmm, it's very simple idea from functions. Function takes number from domain(the set of numbers for which you want the function to work on) , works on it , and gives you number in the codomain or range(both essentially mean the numbers you get from function). Inverse function takes numbers from codomain or range of the function, works on it, and gives you numbers in domain of the function.

For our example, tan is function of our angle. it takes angles, which is domain, and gives you their tangents(opp/adj ratio if they are angle in right triangle), which is the range or codomain. Tan^-1, also known as arctan, takes the tangents,which is codomain of tan, and gives you the angles, which is domain of tan.
Hope that helps :D
• Hey why don't we just write tan^-1(6) instead writing tan^-1(324/54) . Would it be the same answer?
• Yes, you are correct. Most teachers would expect you to simplify the fraction.
• Isn't Cot is the inverse of Tan?
• No. The cotangent is the reciprocal, not the inverse of tangent. The inverse tangent is the arctangent.
NOTE: There is some unfortunate difficulty in notation. If the symbol ⁻¹ comes immediately after the name or symbol of a function, then it does NOT mean the reciprocal: it means the inverse function. But if ⁻¹ comes AFTER some constant, variable or other expression, then it means the reciprocal.

So, again, tan⁻¹ x is NOT equal to 1/tan x and so it is NOT the cotangent.
• What angle would he have to aim IF the laser beam was affected by gravity?
• Laser beams are affected by gravity. But so minutely that the effect wouldn't appear in the second decimal place of the angle. So the answer would be the same.
• This question is mostly relying on calculator. Can you teach us how to do it using your brain, without paper, pencil, or calculator?
• What is the difference between a right and a left triangle?
• Right triangles have a right angle. There are no left triangles.
• if there is a angle given and a side, how do I solve
• Technically, isn't the agent going to shoot the tip of the eiffel tower if he aims at 80.54 degrees? Yes, the alien is tiny but I think his height should be accounted for. Just a side thought.