Question

Determine the remaining sides and angles of the triangle ABC.

A. 18.95 degree.
B. 0.56 degree.
C. 17.83 m.

Answer 1

Angle C ∠C = 160.49°

side b = 0.522 m

side a = 17.34 m

Explanation:

Given that;

In a Δ ABC,

∠A = 18.95°

∠B = 0.56°

∠C = ???

side A = ???

side B = ???

side C = 17.83 m

We are to determine the unknown missing sides and the angle.

We know that, the sum of angles in a triangle = 180°

∴

∠A + ∠B + ∠C = 180°

18.95° + 0.56° + ∠C = 180°

∠C = 180° - 18.95° - 0.56°

∠C = 160.49°

Using sine rule to determine the unknown sides. The sine rule can be expressed as:

`\mathtt{(sin \ A)/(a) = (sin \ B)/(b) = (sin \ C)/(c) }`

To determine side b, we have:

`\mathtt{ (sin \ B)/(b) = (sin \ C)/(c) }`

`\mathtt{ (sin \ 0.56^0)/(b) = (sin \ 160.49)/(17.83) }`

`\mathtt{ b (sin \ 160.49) = 17.83 (sin \ 0.56)}`

`\mathtt{ b = (17.83 (sin \ 0.56))/((sin \ 160.49))}`

`\mathtt{ b = (17.83 * 0.0097737)/(0.33397)}`

`\mathtt{ b = (0.174265071)/(0.33397)}`

b = 0.522 m

For side a, we have

`\mathtt{(sin \ A)/(a) = (sin \ B)/(b) }`

`\mathtt{(sin \ 18.95)/(a) = (sin \ 0.56)/(0.522) }`

`\mathtt{a * sin \ 0.56 = 0.522 (sin \ 18.95)}`

`\mathtt{a = (0.522 (sin \ 18.95))/( sin \ 0.56)}`

`\mathtt{a = (0.522* 0.3247 )/( 0.0097737)}`

a = 17.34 m