Question
In a $\triangle\text{ABC},\angle\text{B}=90^\circ,\text{AB}=24\text{cm}$ and BC = 7cm.
Find:
Find:
- $\sin\text{A}$
- $\cos\text{A}$
- $\sin\text{C}$
- $\cos\text{C}.$
✓
Answer
By pythagoras theoram, we have
$\text{AC}^2 = \text{AB}^2 - \text{BC}^2$
$\Rightarrow\text{AC}^2=(24)^2+(7)^2$
$\Rightarrow\text{AC}^2=576+49=625$
$\Rightarrow\text{AC}=25\text{cm}$
Now, For T-Ratios of $\angle\text{A},$ base = AB and perpendicular = BC
- $\sin\text{A}=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}$
- $\cos\text{A}=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$
- $\sin\text{C}=\frac{\text{AB}}{\text{AC}}=\frac{24}{25}$
- $\cos\text{C}=\frac{\text{BC}}{\text{AC}}=\frac{7}{25}.$
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