Tutoring Summary (20250123OF)

Tutoring Summary (2025-01-23)

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Overview

• Graphs: ★★★★☆
• Trigonometry: ★★★☆☆
  • Naming sides/properties of a triangle.
  • Finding sides/angles with “SOH CAH TOA”.
  • Finding sides with Pythagoras’ Theorem.
  • Finding the area of a triangle (half a square).
• Numbers: ★★★☆☆
• Algebra: ★★★☆☆ ← Next time!
• Ratio: ★★☆☆☆
• Geometry: ★★☆☆☆
• Probability: ★☆☆☆☆
• Statistics: ★☆☆☆☆

Notes

Finding Angles

• Total angles within a triangle add up to $180^{\circ }$. This means we can find the other angles by taking away from $180^{\circ }$!
• We can also use SOH CAH TOA (e.g. $\sin (\theta )=\frac{\text{opposite}}{\text{hypotenuse}}$).
  • We cross off each side we have from SOH CAH TOA (where O is the opposite, A is the adjacent, and H is the hypotenuse). For example, crossing off A and H.
  • Only one of them should have two sides crossed off - that’s the formula we use! For example, if we crossed off A and H then we used C: cosine!
  • When we have the formula, then we can substitute everything in and re-arrange: more on that next session.

Finding Sides

• If we have two sides then we can use Pythagoras’ Theorem!
  • To find the longest side (hypotenuse): $c=\sqrt{a^2+b^2}$.
  • To find one of the other sides: $a=\sqrt{c^2-b^2}\text{or}b=\sqrt{c^2-a^2}$.
  • If you’re curious, you can prove this quite easily with actual squares - maybe watch a video on it :)
• We can use SOH CAH TOA for this, too.
  • Just follow the same steps as before, but also cross off S, C, and T (since we should have an angle, too!).
  • Then, choose which function to use (sine, cosine, or the tan one), substitute and solve! Again, more on this next session.

Finding Area

• Super easy, just pretend it’s a square and half it! So, half the base times height: $A=\frac{1}{2}bh$.

Questions

• Pythagoras questions.
• Trigonometry questions.