Finding Vector Components using Trigonometry

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SUMMARY

The discussion focuses on calculating the X and Y components of a vector using trigonometric functions. The hypotenuse of the triangle is given as 147 km, with an angle of 71.2 degrees. The correct approach involves using the sine function for the vertical component (Fy) and the cosine function for the horizontal component (Fx). The final calculated values are Fx = 47.4 km and Fy = 139 km, which are confirmed as accurate by other participants in the discussion.

PREREQUISITES
  • Understanding of basic trigonometric functions: sine and cosine
  • Familiarity with the Pythagorean theorem
  • Knowledge of vector representation in physics
  • Ability to interpret angles in degrees
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  • Study the application of sine and cosine in vector decomposition
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This discussion is beneficial for physics students, educators, and anyone involved in solving vector-related problems using trigonometry.

C42711
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By c42711 at 2011-10-30

I am supposed to find the X and Y components of the above vector. What I tried to do first was dot in a line, forming a triangle. I then tried to find the length of that line using tangent. I got 431.8, but I am not sure that is right. Next, I used the Pythagorean theorem to try to find the X and Y components, I got some crazy numbers, so I know I'm doing something wrong. Any help would be fantastic. Please & thank you.:)
 
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Tangent is not the correct function to use. 147km is the hypotenuse of the triangle.
 
You'd need to use sine for the vertical and cosine for the horizontal. The sine of the angle is y / the hypotenuse, so y = sin71.2 * h. Similarly, x = cos71.2 * h. Hope that helps.
 
So I tried that and got:
Fx= 47.4 km
Fy= 139 km

Does that seem correct?
 
Yeah, those are the correct values.
 
Than you so much, you're the best.:)
 

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