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

d

Explanation:

The law of Sines applied to a Δ ABC is

`(a)/(sinA)` =
`(b)/(sinB)` =
`(c)/(sinC)`

Using this in Δ HJL

`(z)/(sinL)` =
`(y)/(sinH)` → (b)

Which may be expressed in reciprocal form as

`(sinL)/(z)` =
`(sinH)/(y)` → (a)

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

Answer 2

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

Explanation:

`\sf \displaystyle sin(\theta) =(opposite)/(hypotenuse )`

`\sf \displaystyle sin(L) =(x)/(y)`

`\sf \displaystyle sin(H) =(x)/(z)`

`\displaystyle \sf (sinL)/(z) =(sinH )/(y)`

`\displaystyle \sf ((x)/(y) )/(z) =((x)/(z) )/(y)`

Simplifying the expression.

`\sf \displaystyle (x)/(yz ) = (x)/(yz) \ (true)`

`\displaystyle \sf (z)/(sinL) =(y)/(sinH)`

`\displaystyle \sf (z)/((x)/(y)) =(y)/((x)/(z))`

Multiplying both sides by x.

`\sf yz=yz \ (true)`