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Sagot :
Answer:
74.3 and 105.7
Step-by-step explanation:
In ΔUVW, v = 39 inches, u = 37 inches and ∠U=66°. Find all possible values of ∠V, to the nearest 10th of a degree.
U
V
W
u = 37
v = 39
66°
?°
\frac{\sin A}{a}=\frac{\sin B}{b}
a
sinA
=
b
sinB
From the reference sheet (reciprocal version).
\frac{\sin V}{39}=\frac{\sin 66}{37}
39
sinV
=
37
sin66
Plug in values.
\sin V=\frac{39\sin 66}{37}\approx 0.9629263
sinV=
37
39sin66
≈0.9629263
Evaluate.
V=\sin^{-1}(0.9629263)\approx 74.35\approx 74.3^{\circ}
V=sin
−1
(0.9629263)≈74.35≈74.3
∘
Inverse sine and round.
\text{Quadrant II: } 180-74.3=105.7^{\circ}
Quadrant II: 180−74.3=105.7
∘
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.
66+74.3=140.3^{\circ}\leftarrow \text{Possible}
66+74.3=140.3
∘
←Possible
Less than 180.
66+105.7=171.7^{\circ}\leftarrow \text{Possible}
66+105.7=171.7
∘
←Possible
Less than 180.
\text{Answer: }74.3^{\circ}\text{ and } 105.7^{\circ}
Answer: 74.3
∘
and 105.7
∘
The possible value of the angle XV, to the nearest 10th of a degree in the triangle UVW, where v = 39 inches, u = 37 inches and ZU=66º is 74.4°
What is the law of sine?
The law of sine is nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
Here (A,B,C) are the angle of the triangle and (a,b,c) are the sides of that triangle.
In triangle UVW,
- v = 39 inches,
- u = 37 inches
- Angle U=66º.
Put the values in the formula of sine law,
[tex]\dfrac{\sin V}{v}=\dfrac{\sin U}{u}\\\dfrac{\sin V}{39}=\dfrac{\sin 66}{37}\\\sin V=\dfrac{\sin 66}{37}\times39\\V=\sin^{-1}(0.9629)\\V\approx 74.4^o[/tex]
Thus, the possible value of the angle XV, to the nearest 10th of a degree in the triangle UVW, where v = 39 inches, u = 37 inches and ZU=66º is 74.4°
Learn more about the sine law here;
https://brainly.com/question/2264443
#SPJ2
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