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

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

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

$AB=91.87 m$

Answer 2

The distance AB across the river is approximately 92 m.

The sum of angles in a triangle equals 180°. Therefore,

∠B = 111 degrees 20 minutes = 111.33°

∠C = 12 degrees 15 minutes = 12.25°

Therefore,

∠A + ∠B + ∠C = 180°

∠A + 111.33° +  12.25° = 180

∠A = 180 - 12.25 + 111.33

∠A = 56.42°

AB = ?

BC = 361 m

Using sine rule,

AB / sin 12.25  = 361 / sin 56. 42

cross multiply

AB sin 56. 42 = 361 sin 12.25

AB = 76.5961396485 / 0.83098446927

AB = 92.1751759276

AB ≈ 92 m

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