Question

Find sin a and cos b triangle is right angle

Answer 1

Step-by-step 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)

`sin\text{ A}=\text{ }(opposite)/(hypotenuse)`

Triangle is a right angle

`\begin{gathered} sin\text{ A = }(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 = }√(20)\text{ = }√(4*5) \\ a\text{ = 2}√(5) \end{gathered}`
`\begin{gathered} sin\text{ A = }(2√(5))/(6) \\ sin\text{ A = }(√(5))/(3)\text{ } \end{gathered}`