Question

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

Answer 1

Answer:

Therefore,

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

Step-by-step 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,

$\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}$

substituting the given values we get

$\dfrac{a}{\sin A}= \dfrac{b}{\sin B}$

$\dfrac{10}{\sin A}= \dfrac{17}{\sin 53}\\\\\sin A=0.469\\A=\sin^{-1}(0.469)=28.02\approx 28\°$

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

$\dfrac{b}{\sin B}= \dfrac{c}{\sin C}$

Substituting the values we get

$\dfrac{17}{\sin 53}= \dfrac{c}{\sin 99}\\\\c=21.02\approx 21\ unit$

Therefore,

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