For the triangle described below, solve for B . Apply the rules regarding the use of significant digits after all computations are complete. ft, ft
A) or
C) or
E)no solutions

Question

For the triangle described below, solve for B . Apply the rules regarding the use of significant digits after all computations are complete.   ft,   ft ​
A) or 
C) or 
E)no solutions

Quizplus · Accepted Answer

Using the Law of Cosines, we have:

$B = \cos^{-1}\left(\frac{11ebf5ef\_bbcb\_65a9\_95d1\_b5837b1a0bd4\_TBX9354\_11^2 + 11ebf5ef\_bbcb\_65ad\_95d1\_e5fb87034b5d\_TBX9354\_11^2 - 2 	imes 11ebf5ef\_bbcb\_65a8\_95d1\_89dcadbd4190\_TBX9354\_11 	imes 11ebf5ef\_bbcb\_65a9\_95d1\_b5837b1a0bd4\_TBX9354\_11 	imes \cos(A)}{11ebf5ef\_bbcb\_65ad\_95d1\_e5fb87034b5d\_TBX9354\_11 	imes 2}ight)$

Substituting the given values, we get:

$B = \cos^{-1}\left(\frac{(11.6\ ft)^2 + (10.6\ ft)^2 - 2 	imes (11\ ft)(11.6\ ft)\cos(40^\circ)}{10.6\ ft 	imes 2}ight) \approx \cos^{-1}(0.201) \approx 78.5^\circ$

Using the rules of significant digits, the final answer should have the same number of decimal places as the measurement with the least number of decimal places, which is 10.6 ft. Therefore, the answer is B) 11ebf5ef_bbcb_65ac_95d1_0796c0b4dc63_TBX9354_11 or 11ebf5ef_bbcb_65ad_95d1_e5fb87034b5d_TBX9354_11.

For the Triangle Described Below, Solve for B