Refer to right triangle ABC with C = 90^{circ}. Begin each problem by drawing a picture of the triangle with both the given and asked­for information labeled appropriately. Also, write your answers for angles in decimal degrees. If a = 42.3 inches and b = 32.4 inches, find B

Question
Decimals
asked 2021-01-15
Refer to right triangle ABC with \(C = 90^{\circ}.\) Begin each problem by drawing a picture of the triangle with both the given and asked­for information labeled appropriately.
Also, write your answers for angles in decimal degrees.
If \(a = 42.3\ inches\ and\ b = 32.4\) inches, find B

Answers (1)

2021-01-16
Data analysis
Given right angled triangle at C for a triangle \(\triangle\ ABC.\)
And \(a = 42.3\) inches
\(b = 32.4\) inches
To find angle at B.
The triangle with above data is as follows
image
Solution
Since the give triangle is right angled,
Applying Pythagoras theorem,
\(c^{2} = a^{2}\ +\ b^{2}\)
\(= 42.3^{2}\ +\ 32.4^{2}\)
\(= 1789.29\ +\ 1049.76\)
\(\Rightarrow c =\ \sqrt{2839.05} = 53.2827364\)
Hence the length of \(AB = c = 53.28\) inches
(Rounding to two decimals)
By sine law,
\(\sin\ B = \frac{opposite\ side}{hypotenuse}\)
\(= AC/AB\)
\(= b/c\)
\(= 32.4/53.28\)
\(\Rightarrow\ \angle\ B = \arcsin\ (0.608108) = 37.4528244^{\circ}\)
Hence the angle at B is \(37.24^{\circ}\)
(Rounding to two decimals)
0

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P.vaiue Pevgiue
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\(\begin{array}{|c|c|}\hline \text{Subject number} & \text{Protetion concentration} \\ \hline 1 & 1.4 \\ \hline 2 & 2.4 \\ \hline 3 & 2.4 \\ \hline 4 & 3.3 \\ \hline 5 & 4.4 \\ \hline 6 & 4.7 \\ \hline 7 & 6.7 \\ \hline 8 & 7.9 \\ \hline 9 & 9.5 \\ \hline 10 & 11.7 \\ \hline \end{array}\)
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...