In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C ?

In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C ?

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Solution:

⇨ In △ ABC

Exercise 8.1 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C Solution:

⇨ From Pythagoras Theorem

$In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C ?$

$\large \therefore AC^2=AB^2+BC^2$

$\large \Rightarrow AC^2=24^2+7^2$

$\large \Rightarrow AC^2=576+49$

$\large \Rightarrow AC^2=625$

$\large \Rightarrow AC^2=25^2$

$\large \Rightarrow AC=25 cm$

(i) sin A, cos A

Solution:

$\large sin A=\frac{p}{h}=\frac{BC}{AC}=\frac{7}{25}$

$\large cos A=\frac{b}{h}=\frac{AB}{AC}=\frac{24}{25}$

(ii) sin C, cos C

Solution:

$\large sin C=\frac{p}{h}=\frac{AB}{AC}=\frac{24}{25}$

$\large cos C=\frac{b}{h}=\frac{BC}{AC}=\frac{7}{25}$