Question

To find the distance AB across a river, a surveyor laid off a distance BC=361 m on one side of the river. It is found that B=111 degrees 20 minutes and C=12 degrees 15 minutes. Find AB

Answer 1

Answer:

91.87m

Step-by-step explanation:

We are given that

BC=361 m

Angle B=$111^{\circ}20'=111+\frac{20}{60}=111.33^{\circ}$

1 degree= 60 minute

Angle C=$12^{\circ} 15'=12+\frac{15}{60}=12.25^{\circ}$

We have to find the value of AB.

Sum of angles of triangle=180 degrees

$\angle A+\angle B+\angle C=180$

$\angle A=180-(\angle C+\angle B)=180-(111.33+12.25)=56.42^{\circ}$

By using law of sine

$\frac{AB}{sin C}=\frac{BC}{sin A}$

$AB=\frac{BCsin C}{sin A}=\frac{361 sin 12.25^{\circ}}{sin 56.42^{\circ}}$

$AB=91.87 m$