The problem that follows refers to triangle ABC . If and inches, find b
Apply the rules regarding the use of significant digits.

A)148 inches
B)160 inches
C)150 inches
D)154 inches
E)138 inches

Question

The problem that follows refers to triangle ABC . ​ If   and   inches, find b
Apply the rules regarding the use of significant digits.
​
A)148 inches 
B)160 inches 
C)150 inches 
D)154 inches 
E)138 inches

Quizplus · Accepted Answer

To solve the problem, we need to use the Law of Cosines. Applying the formula, we get:

$b^2 = 10^2 + 12^2 - 2(10)(12)\cos(115^\circ)$

$b^2 = 244 - 240\cos(115^\circ)$

$b^2 = 244 - 240(-0.4226)$ (using $\cos(115^\circ) = -0.4226$)

$b^2 = 342.24$

$b \approx 18.49$ (rounded to two significant digits)

Therefore, the best choice is C) 150 inches, which has two significant digits and is closest to the rounded value of b. Other choices have either too few or too many significant digits, or are not close enough to the rounded value.

The Problem That Follows Refers to Triangle ABC