Topic Content:
- Solving Right-Angled Triangles
Sometimes it is useful to use both trigonometric ratios and Pythagoras rule to solve a right-angled triangle.
Solving a right-angled triangle means finding the unknown sides and angles.
For example in ΔABC shown below:
by Pythagoras theorem
|BC|2 = |AB|2 + |AC|2
Sin B = \( \frac{Opp}{Hyp} = \frac{b}{a} \)
Sin C = \( \frac{Opp}{Hyp} = \frac{c}{a} \)
Cos B = \( \frac{Adj}{Hyp} = \frac{c}{a} \)
Cos C = \( \frac{Adj}{Hyp} = \frac{b}{a} \)
Tan B = \( \frac{Opp}{Adj} = \frac{b}{c} \)
Tan C = \( \frac{Opp}{Adj} = \frac{c}{a} \)
Example 3.5.1:
One side of an equilateral triangle XYZ is 10 cm long. Find its altitude XL to the nearest whole number.
Solution
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