Question

A memorial is V-shaped with equal sides of length 258.75 ft. The angle between these sides measures 126°12'. Find the distance between the ends of the two sides. 126°12) 258.75 258.75 The distance between the ends of the two sides ist (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Answer 1

Solution:

C b C 126°12 258.75 258.75 A A

$A = 126^{\circ}12' = 126^{\circ} + (12/60)^{\circ}=126^{\circ}+0.2^{\circ}=126.2^{\circ}$

A = 126.2

In triangle (side-angle-side) ABC, using cosine law,

$a^{2}=b^{2}+c^{2}-2bc\times cosA$

$a^{2}=(258.75)^{2}+(258.75)^{2}-2\times 258.75\times 258.75\times cos(126.2^{\circ})$

$a^{2}=66951.5625+66951.5625-133903.125\times (-0.5906)$

$a^{2}=212986.3106$

$a=461.50$

The distance b/w two ends is 461.50 ft