Answer:
Explanation:
Given:
Triangle ABC with 3 sides given
To find:
a) sinA
b) cos B
a) To find sin A, we will use sine ratio (SOH)
[tex]sin\text{ A}=\text{ }\frac{opposite}{hypotenuse}[/tex]
Triangle is a right angle
[tex]\begin{gathered} sin\text{ A = }\frac{a}{6} \\ \\ To\text{ get a, we will apply pythagoras theorem:} \\ hyp^2=\text{ opp}^2\text{ + adj}^2 \\ 6^2\text{ = a}^2\text{ + 4}^2 \\ a^2\text{ = 6}^2-\text{ 4}^2\text{ = 36 - 16} \\ a^2\text{ = 20} \\ \text{a = }\sqrt{20}\text{ = }\sqrt{4\times5} \\ a\text{ = 2}\sqrt{5} \end{gathered}[/tex][tex]\begin{gathered} sin\text{ A = }\frac{2\sqrt{5}}{6} \\ sin\text{ A = }\frac{\sqrt{5}}{3}\text{ } \end{gathered}[/tex]
