Question

In scalene triangle ABC shown in the diagram below, m2C = 90°.B.Which equation is always true?sn A = sin Bcos sn A = cos BCanAB4 5 678 9 1011

Answer 1

inNote: To know which equation is true, then we will have to TEST for each of the choices we are to pick from.

From the tirangle in the image.

`\begin{gathered} 1)\sin \text{ A =}\frac{\text{ Opp}}{\text{Hyp}}\text{ = }(a)/(c) \\ \cos \text{ B = }\frac{\text{ADJ}}{\text{HYP}}\text{ = }(a)/(c) \\ So\text{ from the above, we can s}ee\text{ that: SinA = Cos B :This mean the choice are equal} \\ \end{gathered}`
`\begin{gathered} 2)\text{ To test for the second choice we have..} \\ \text{ Cos A = Cos B} \\ \text{for Cos A =}\frac{\text{Adj}}{\text{Hyp}}\text{ =}(b)/(c) \\ \\ \text{for Cos B = }\frac{Adj}{\text{Hyp}}\text{ = }(a)/(c) \\ \text{from here we can s}ee\text{ that Cos A }\\e\text{ Cos B : meaning Cos A is not equal to Cos B} \\ \end{gathered}`

3) To test for the third choice: Sin A = Cos A

`\begin{gathered} \sin \text{ A=}\frac{opp}{\text{Hyp}}\text{ = }(a)/(c) \\ \cos \text{ A = }\frac{Adj}{\text{Hyp}}\text{ = }(b)/(c) \\ we\text{ can s}ee\text{ that sinA }\\e\text{ cos }A,\text{ This mean they are not equal} \end{gathered}`
`\begin{gathered} 4)\text{ To test if: tan A = sin B} \\ \text{ }tan\text{ A = }\frac{opp}{\text{Adj}}\text{ = }(a)/(b) \\ \\ \text{ sin B = }\frac{Opp}{\text{Hyp}}\text{ = }(b)/(c) \\ so\text{ from what we have, w can s}ee\text{ that tan A }\\e\text{ sinB: Meaning they are not equal.} \end{gathered}`

Meaning the first choice is the answer that is sin A = CosB