Can someone please check my working to this proof

  • Context: Graduate 
  • Thread starter Thread starter chris99191
  • Start date Start date
  • Tags Tags
    Proof
Click For Summary
SUMMARY

The proof demonstrates that the height of point P above the floor after tilting the crate is expressed as h(cosb + 2sinb). The calculations involve determining the length of OP as h√5, with sin(a) equal to 1/√5 and cos(a) equal to 2/√5. The final equation is derived using the sine addition formula, confirming the correctness of the proof.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with the sine addition formula.
  • Knowledge of basic geometry, particularly in relation to right triangles.
  • Ability to manipulate algebraic expressions involving square roots.
NEXT STEPS
  • Study the sine addition formula in depth.
  • Explore geometric proofs involving right triangles.
  • Learn about the properties of trigonometric functions in various quadrants.
  • Practice deriving equations from geometric configurations.
USEFUL FOR

Students in mathematics, particularly those studying trigonometry and geometry, as well as educators looking for examples of geometric proofs.

chris99191
Messages
9
Reaction score
0
I completed this proof in the attachment but can someone please check my working

The aim was to show that the height of P above floor after the crate is tilted is h(cosb+2sinb)

From the rectangles you can work out
Length of OP=h√5
sin(a)=1/√5
cos(a)=2/√5

therefore
height=h√5.sin(a+b)
=h√5.(sinacosb+cosasinb)
=h√5.(1/√5cosb+2/√5sinb)
=h(cosb+2sinb)
 

Attachments

  • Trig.jpg
    Trig.jpg
    4.9 KB · Views: 489
Last edited:
Mathematics news on Phys.org
Yes, its right
 

Similar threads

Replies
2
Views
1K
Replies
5
Views
2K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
11
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 1 ·
Replies
1
Views
3K