1) Suppose that a company will select 3 people from a collection of 15 applicants to serve as a regional manager, a branch manag
1 answer:
Answer:
2,730 ways
Step-by-step explanation:
Since the same person cannot hold more than one position, the company has 15 options for the first choice, 14 for the second choice and 13 for the third choice, and since the three chosen positions are different, the order of the picks also matter. The number of ways the selection can be made is:
The selection can be made in 2,730 ways.
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Answer:
A. single triangle. C = 8.74°, A = 1.26°, a = 1.01
Step-by-step explanation:
When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.
<h3>Law of Sines</h3>The law of sines tells us the sides and angles have the relation ...
sin(A)/a = sin(B)/b = sin(C)/c
We can use this first to find angle C:
sin(C) = c/b·sin(B)
C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°
∠C ≈ 8.74°
<h3>Remaining measures</h3>Now that we know two angles, we can find the third:
A = 180° -B -C = 180° -170° -8.74° = 1.26°
∠A = 1.26°
Using the law of sines again, we can find the measure of side 'a'.
a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346
The measure of segment 'a' is about 1.01 units.
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<em>Additional comment</em>
If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.
