Question

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

Answer 1

Answer: Choice C

x/w and z/(y+v)

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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.

Answer 2

Answer:

$\frac{x}{w}, \: \frac{z}{y+v}$

Step-by-step explanation:

sin θ = $\frac{opposite}{hypotenuse}$

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

sin ∠ABD = $\frac{x}{w}$

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

sin ∠ABD = $\frac{z}{y+v}$