Question

Please help me with this question with full solutions!!!

Answer 1

`(x)/(w), \: (z)/(y+v)`

Step-by-step explanation:

sin θ =
`(opposite)/(hypotenuse)`

Let’s take triangle ABD, where w is the hypotenuse.

sin ∠ABD =
`(x)/(w)`

Let’s take triangle ABC (whole triangle), where y + v is the hypotenuse.

sin ∠ABD =
`(z)/(y+v)`

Answer 2

Answer: Choice C

x/w and z/(y+v)

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Step-by-step explanation:

All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.

Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).

So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w

x/w is one of the answers

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Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z

Therefore,

sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)

z/(y+v) is the other answer

Side note: triangle ACD is not used at all.