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

Globokim8 2021-01-15 Answered
Refer to right triangle ABC with C=90. 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
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Expert Answer

Elberte
Answered 2021-01-16 Author has 95 answers

Data analysis
Given right angled triangle at C for a 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,
c2=a2 + b2
=42.32 + 32.42
=1789.29 + 1049.76
c= 2839.05=53.2827364
Hence the length of AB=c=53.28 inches
(Rounding to two decimals)
By sine law,
sin B=opposite sidehypotenuse
=AC/AB
=b/c
=32.4/53.28
  B=arcsin (0.608108)=37.4528244
Hence the angle at B is 37.24
(Rounding to two decimals)

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