Question

A man claims that his lot is triangular, with one side 450 m long and the adjacent side 200 m long. The


angle opposite one side is 28º. Determine the other side length of this lot to the nearest metre.

Answer 1

Answer:

545 m

Step-by-step explanation:

Set A = 28º, B as the angle between the 450 m and 200 m side, and C as the remaining angle. Then:

AB = 200 m

BC = 450 m

According to the law of sines:

$\frac{450}{sin(28)}=\frac{110}{sin(C)} \\sin(C) = \frac{110}{450}*0.469\\ C= 6.6^o$

The remaining angle is then:

$B= 180-28-6.6\\B=145.4^o$

Applying the law of sines again:

$\frac{450}{sin(28)}=\frac{AC}{sin(145.4)} \\AC= \frac{450}{0.469}*0.568\\ AC= 545\ m$

To the nearest meter, the other side is 545 meters long.