Answer:
A.
Step-by-step explanation:
We have been given a diagram. We are asked to find the measure of angle ABC.
First of all, we will find measure of major arc AC by subtracting 146 from 360 degrees.
Now, we will use tangent-tangent angle theorem to solve for ABC.
Tangent-Tangent angle theorem states that angle formed by two tangents outside a circle is half the difference of intercepted arcs.
Therefore, the measure of angle ABC is 34 degrees and option A is the correct choice.
Answer:
39.5 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle.
Tan = Opposite/Adjacent
This lets us write two equations in two unknowns:
tan(67°) = AD/CD . . . . . . . . . . angle at guy point
tan(39°) = AD/(CD+32) . . . . . .angle 32' farther
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Solving the first equation for CD and using that in the second equation, we can get an equation for AD, the height of the tower.
CD = AD/tan(67°)
tan(39°)(CD +32) = AD . . . . eliminate fractions in the second equation
tan(39°)(AD/tan(67°) +32) = AD
32·tan(39°) = AD(1 -tan(39°)/tan(67°)) . . . simplify, subtract left-side AD term
32·tan(39°)tan(67°)/(tan(67°) -tan(39°)) = AD . . . . divide by AD coefficient
AD ≈ 39.486 . . . . feet
The tower is about 39.5 feet high.
Answer:
Step-by-step explanation:
First of all we need to know when does two events become independent:
For the two events to be independent, that is if condition on one does not effect the probability of other event.
Here, in our case the only option that satisfies the condition for the events to be independent is . Rest are not in accordance with the definition of independent events.