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research73
26.04.2021 •
Mathematics
In ΔSTU, s = 580 inches, u = 440 inches and ∠U=17°. Find all possible values of ∠S, to the nearest 10th of a degree.
S
T
U
s = 580
u = 440
?°
17°
\frac{\sin A}{a}=\frac{\sin B}{b}
a
sinA
=
b
sinB
From the reference sheet (reciprocal version).
\frac{\sin S}{580}=\frac{\sin 17}{440}
580
sinS
=
440
sin17
Plug in values.
\sin S=\frac{580\sin 17}{440}\approx 0.3853991
sinS=
440
580sin17
≈0.3853991
Evaluate.
S=\sin^{-1}(0.3853991)\approx 22.669\approx 22.7^{\circ}
S=sin
−1
(0.3853991)≈22.669≈22.7
∘
Inverse sine and round.
\text{Quadrant II: } 180-22.7=157.3^{\circ}
Quadrant II: 180−22.7=157.3
∘
Sine is positive in quadrants 1 and 2.
\text{Check for possibility:}
Check for possibility:
No triangle's angles may add to more than 180.
17+22.7=39.7^{\circ}\leftarrow \text{Possible}
17+22.7=39.7
∘
←Possible
Less than 180.
17+157.3=174.3^{\circ}\leftarrow \text{Possible}
17+157.3=174.3
∘
←Possible
Less than 180.
\text{ }22.7^{\circ}\text{ and } 157.3^{\circ}
22.7
∘
and 157.3
∘
Solved
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Ответ:
Ответ:
Option C) is the correct answer.
Step-by-step explanation:
We are given the following in the question:
Mean = 192
Sample mean,
= 212
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 56.5
95% Confidence interval:
Putting the values, we get,
Thus, the correction answer is
Option C)
"The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we have support for the results of the May 2011 study."