Question

Solve for all missing posts of triangles with the given information. B =53 degrees, a =10, b=17

Answer 1

Therefore,

`m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units`

Explanation:

Consider a Δ ABC with

m∠ B = 53°

BC = a = 10

AC = b = 17

To Find:

AC = c = ?

m∠ A = ?

m∠ C = ?

Solution:

We know in a Triangle Sine Rule Says that,

In Δ ABC,

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

substituting the given values we get

`(a)/(\sin A)= (b)/(\sin B)`

`(10)/(\sin A)= (17)/(\sin 53)\\\\\sin A=0.469\\A=\sin^(-1)(0.469)=28.02\approx 28\°`

Therefore m∠A = 28°

Triangle sum property:

In a Triangle sum of the measures of all the angles of a triangle is 180°.

`\angle A+\angle B+\angle C=180\\\\28+53+\angle C=180\\\therefore m\angle C =180-81=99\°`

Therefore m∠C = 99°

Now From Sine rule we have

`(b)/(\sin B)= (c)/(\sin C)`

Substituting the values we get

`(17)/(\sin 53)= (c)/(\sin 99)\\\\c=21.02\approx 21\ unit`

Therefore,

`m\angle A =28\°\\\\m\angle C =99\°\\\\c=21\ units`