Trigonometry and Triangle Questions

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    Triangle Trigonometry
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SUMMARY

This discussion focuses on solving various trigonometry problems related to triangles, specifically using the sine definition and properties of right-angled and isosceles triangles. Key techniques mentioned include the sine law for solving triangle dimensions and the application of trigonometric ratios. Additionally, the area of a triangle can be derived using trigonometric principles, although a formula for decay was mistakenly included, indicating a potential misunderstanding of the topic. The discussion emphasizes foundational trigonometric concepts necessary for solving these types of problems.

PREREQUISITES
  • Understanding of trigonometric ratios, specifically sine, cosine, and tangent.
  • Familiarity with properties of right-angled and isosceles triangles.
  • Knowledge of the sine law for triangle calculations.
  • Basic understanding of area calculation for triangles using trigonometry.
NEXT STEPS
  • Study the applications of the sine law in various triangle problems.
  • Learn how to derive the area of a triangle using trigonometric functions.
  • Explore the relationship between angles and sides in right-angled triangles.
  • Investigate common trigonometric identities and their applications in problem-solving.
USEFUL FOR

Students, educators, and anyone looking to strengthen their understanding of trigonometry, particularly in relation to triangle calculations and properties.

kingsala
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Gents, Thanks for all the guidance in the past with my work and brothers too.

Can anyone help with these , see file attached
 

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Edit: I have attached the PDF pages as images for those who don't wish to download a PDF attachment :)What do you know about trigonometry?

Q1) You can solve this one by using the definition of sine: $$\sin \theta = \frac{opp}{hyp}$$ (the SOH of SOHCAHTOA if you were taught this mnenomic)

Q2) This is both a right angled and isoceles triangle. Since the sum of angles is 180 degrees and one is 90 you can find the other two (they're the same remember)

Q3) This can be solved using one of the trig ratio

Q4) Use the sine law:
$$\dfrac{\sin A}{A} = \dfrac{\sin B}{B} = \dfrac{\sin C}{C}$$

Q5) Do you know how to find the area of a triangle from trig?
$$A = \frac{1}{2}ab\sin(C)$$

Q6) The usual formula for decay is [math]A = A_0(1-r)^t[/math]. Not sure why it's here as not trig related
 

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