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kirill [66]
3 years ago
7

Solve the triangle. A = 32°, a = 19, b = 14

Mathematics
1 answer:
Paha777 [63]3 years ago
8 0

Answer:

A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36

Step-by-step explanation:

We have two sides of the triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the sine theorem to find the angle B.

We know that according to the sine theorem it is true that:

\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}

\frac{sin(32\°)}{19}=\frac{sin(B)}{14}

sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°

We know that the sum of the internal angles of a triangle is always equal to 180.

So:

C=180-32-22.98\\\\C=125.02\°

Finally we find the c side

\frac{sin(A)}{a}=\frac{sin(C)}{c}

\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}

0.02789=\frac{sin(125.02)}{c}

c=\frac{sin(125.02)}{0.02789}\\\\c=29.36

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  • 3. E) -0.8
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=========================================

Explanations:

3. We have negative correlation because the regression line is going downhill (move from left to right). The points are fairly close to the same regression line, so I'd say we have either moderate or fairly strong negative correlation. That means r is fairly close to -1. It's not -1 exactly since that would have to mean all points are on the same line.

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4. Negative correlation goes with negative r values. Refer to problem 3. Positive correlation goes to positive r values. The r value will most likely not equal the slope value, but they share the same sign.

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