Question

the Red Line in the figure is an altitude of triangle hjl. Using right angle trig and properties of equality, y sin L = x = z sin H, write the Law of Sines for this triangle
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Answer 1

Answer:

$\Large \boxed{\mathrm{\bold{C}}}$

Step-by-step explanation:

$\sf \displaystyle sin(\theta) =\frac{opposite}{hypotenuse }$

$\sf \displaystyle sin(L) =\frac{x}{y}$

$\sf \displaystyle sin(H) =\frac{x}{z}$

$\displaystyle \sf \frac{sinL}{z} =\frac{sinH }{y}$

$\displaystyle \sf \frac{\frac{x}{y} }{z} =\frac{\frac{x}{z} }{y}$

Simplifying the expression.

$\sf \displaystyle \frac{x}{yz } = \frac{x}{yz} \ (true)$

$\displaystyle \sf \frac{z}{sinL} =\frac{y}{sinH}$

$\displaystyle \sf \frac{z}{\frac{x}{y}} =\frac{y}{\frac{x}{z}}$

Multiplying both sides by x.

$\sf yz=yz \ (true)$

Answer 2

Answer:

d

Step-by-step explanation:

The law of Sines applied to a Δ ABC is

$\frac{a}{sinA}$ = $\frac{b}{sinB}$ = $\frac{c}{sinC}$

Using this in Δ HJL

$\frac{z}{sinL}$ = $\frac{y}{sinH}$ → (b)

Which may be expressed in reciprocal form as

$\frac{sinL}{z}$ = $\frac{sinH}{y}$ → (a)

Thus the law of Sines can be expressed as either (a) or (b)