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3 years ago

Some help figuring out the answer?? Also explain a little how you got there

Mathematics

1 answer:

ipn [44]3 years ago

6 0

9514 1404 393

Answer:

x = 10·cos(θ) -4·cot(θ)

Step-by-step explanation:

Apparently, we are to assume that the horizontal lines are parallel to each other.

The relevant trig relations are ...

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

If the junction point in the middle of AB is labeled X, then we have ...

sin(θ) = 4/BX ⇒ BX = 4/sin(θ)

cos(θ) = x/XA ⇒ XA = x/cos(θ)

Then ...

BX +XA = AB = 10

Substituting for BX and XA using the above relations, we get

4/sin(θ) +x/cos(θ) = 10

Solving for x gives ...

x = (10 -4/sin(θ))·cos(θ)

x = 10·cos(θ) -4·cot(θ) . . . . . simplify

_____

We used the identity ...

cot(θ) = cos(θ)/sin(θ)

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