The problem that follows refers to triangle ABC . If and yd, find a
Apply the rules regarding the use of significant digits after all computations are complete.

Question

The problem that follows refers to triangle ABC . ​ If   and   yd, find a
Apply the rules regarding the use of significant digits after all computations are complete.
​

Quizplus · Accepted Answer

​Using the Law of Cosines, we have:
$ab^2 + bc^2 - 2abcos(\angle ABC) = ac^2$
$11^2 + 13^2 - 2\cdot 11\cdot 13cos(\angle ABC) = 12^2$
$cos(\angle ABC) = \frac{11^2 + 13^2 - 12^2}{2\cdot 11\cdot 13}$
$cos(\angle ABC) = 0.303$
Using the Law of Sines, we have:
$\frac{11}{sin(\angle ABC)} = \frac{yd}{sin(\angle A)}$
$\frac{13}{sin(\angle ABC)} = \frac{yd}{sin(\angle C)}$
$\frac{11}{sin^{-1}(0.303)} = \frac{13}{sin^{-1}(0.303)} = \frac{yd}{sin(\angle B)}$
$\angle A$ and $\angle C$ are acute angles, so we can use the approximation $sin(	heta) \approx 	heta$ when $	heta$ is small, in radians. Therefore:
$\frac{11}{0.309} \approx 35.6$ yd
$\frac{13}{0.309} \approx 42.1$ yd
$\frac{yd}{0.303} \approx 54.1$ yd
We take the value of $yd$ that has the least number of significant digits, which is the second calculation, giving $yd \approx 42.1$ yd. Thus, the answer is C, 53.1 yd.

The Problem That Follows Refers to Triangle ABC