Walter builds birdhouses. he spends $5 on the materials for each birdhouse. he can build one in 30 minutes. he is semi-retired but earns $8 per hour at the local hardware store. he can sell a birdhouse for $20 each. refer to scenario 13-11. the explicit cost for one birdhouse is

Step-by-step explanation:

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3 years ago

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Use the information given in the diagrams to show that

Vlad1618 [11]

Answer:

d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

Step-by-step explanation:

The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.

<h3>top triangle</h3>

The law of sines applied to the top triangle is ...

BC/sin(A) = AC/sin(θ)

Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...

∠A = 180° -θ -θ = 180° -2θ

A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...

sin(A) = sin(180° -2θ) = sin(2θ)

and our above Law of Sines equation tells us ...

BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)

<h3>bottom triangle</h3>

The law of sines applied to the bottom triangle is ...

DC/sin(B) = BC/sin(D)

d/sin(α) = BC/sin(β)

Multiplying by sin(α) we have ...

d = BC·sin(α)/sin(β)

Using our expression for BC gives the desired relation:

d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))

7 0

2 years ago