Mathematics, 06.07.2019 13:00 andreanb8083

Geometry questiontomorrow i got a test i need

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Answer from: biancaTomas010B

Steps:

So before we can find line BC, we have to find Line BD. To do this, we will be using the pythagorean theorem, which is leg² + leg² = hypotenuse² . In this case, Line BA, which has a value of 16, is our hypotenuse and Lines AD, which has a value of 12, and BD, which has a value of x, are our legs. Set up our equation as such:

12^2+x^2=16^2

Firstly, solve the exponents:

144+x^2=256

Next, subtract both sides by 144:

x^2=112

Next, square root both sides and line BD is √112 units (To get more accurate results, always leave approximation til the end of the problem.)

Now that we have line BD, we are going to be using trig ratios to solve for C. For Trig Ratios, remember "SOH CAH TOA" (θ = an angle)

Sin(θ) = Opposite/HypotenuseCos(θ) = Adjacent/HypotenuseTan(θ) = Opposite/Adjacent

Since line BD does not touch the 40° angle, this makes BD the opposite side. And since line BC touches both the 40° angle and the right angle, this makes line BC the adjacent side. Since we have the opposite side and are solving for the adjacent side, we will be using Tan (or Tangent) to solve for the angle. Set up our equation as such (let y = BC):

$\frac{\tan (40)}{1}=\frac{\sqrt{112}}{y}$

Firstly, cross multiply:

$\sqrt{112}=\tan (40)*y$

Next, divide both sides by tan(40):

12.6=y

Line BC is 12.6 cm.

Answer from: Quest

answer: huh

step-by-step explanation:

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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