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samanthasheets8362
03.04.2020 •
Mathematics
Round to the nearest tenth.
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Ответ:
d. g = 42; E = 37.7°; G = 99.3°
Step-by-step explanation:
Evaluating the problem, you find that the given angle is opposite the longest given side, so you can conclude
there is only one solution (this is NOT an ambiguous case)angle E will be smaller than 43°You can also recognize that the sum of the remaining two angles must be ...
180° -43° = 137°
__
Your next step should be to look at the answer choices to check their feasibility.
a. angle E is more than 43° -- bad answer
b. sum of angles is not 137° -- bad answer
c. none -- bad answer. The triangle will have a solution.
d. sum of angles is 137°, angle E < 43° -- feasible answer
__
You can further check to see if the offered choice makes sense by computing the value of angle E.
From the Law of Sines, you know that ...
sin(E)/e = sin(F)/f
sin(E) = (e/f)sin(F) . . . . . multiply by e
E = arcsin((e/f)sin(F)) ≈ 37.7° . . . . . . . . matches answer choice D
and side g will be ...
g/sin(G) = f/sin(F)
g = f(sin(G)/sin(F)) = 29(sin(137°-37.7°)/sin(43°)) ≈ 41.96
g ≈ 42.0 . . . . . . matches answer choice D
Comment on the solution
You may have noticed we wrote the Law of Sines two ways. One used sine/side, and the other used side/sine. The particular form was chosen to put the unknown in the numerator, making it easier to solve for. Of course, with a little practice, you don't need to write the proportion. You can jump directly to the answer form you need:
E = arcsin(e/f)sin(F))g = f(sin(G)/sin(F))Ответ:
Option B
see the attached figure
Step-by-step explanation:
we know that
Opposite number or additive inverse of any number (n) is a number which, if added to n, results in 0
so
In this problem
The opposite of -1/2 is 1/2
so
point M is 1/2 ----> point M is located in the interval (0,1)
The opposite of 5/2 is -5/2
so
point N is -5/2 ----> point M is located in the interval (-3,-2)
therefore
The correct answer is the option B