# Tutor profile: Delfin B.

## Questions

### Subject: Trigonometry

In $$Δ ABC$$, right-angled at $$B$$, $$AC + BC = 25 cm$$ and $$AB = 5 cm$$. Determine the values of $$\sin A$$, $$\cos A$$ and $$\tan A$$.

In $$Δ ABC$$, right-angled at $$B$$. $$AC + BC = 25 cm$$ and $$AB = 5 cm$$ Let $$BC = x$$ $$cm$$ and $$AC = (25 –x)$$ $$cm$$ Using Pythagoras theorem, $$CA^{2} = CB^{2} + BA^{2} $$ $$⇒ (25 – x)^{2} = (x)^{2} + (5)^{2}$$ $$⇒ 625 -50x + x^{2} = x^{2} + 25 $$ $$⇒ -50x = -600$$ $$⇒ x = 12$$ $$∴ CB = 12 cm$$ and $$CA = 25 – 12 = 13 cm$$ $$\sin A = \frac{CB}{CA} = \frac{12}{13}$$ $$\cos A = \frac{AB}{CA} = \frac{5}{13}$$ $$\tan A = \frac{CB}{AB} = \frac{12}{5}$$

### Subject: Pre-Algebra

Find the value of $$x$$ in $$x - 17 = 100$$

Given the equation $$x - 17 = 100$$ Add $$17$$ to both sides $$x - 17 + 17 = 100 + 17$$ After solving $$x - 0 = 117$$ Answer: $$x = 117$$

### Subject: Algebra

Simplify the algebraic expression $$3 (a -3) + 4 b - 2 (a - b - 3) + 1$$

Given the algebraic expression $$3 (a -3) + 4 b - 2 (a - b - 3) + 1$$ Multiply factors. $$= 3 a - 9 + 4 b - 2 a + 2 b + 6 + 1$$ Group like terms. $$= a + 6 b - 2 $$ Answer: $$ a + 6 b - 2 $$

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