Question

Please help !
Find a.
Round to the nearest tenth:
27 cm
102
28
a = [? ]cm
Law of Sines: sin A
sin C
sin B
b
a
A=?

Answer 1

Given:

In the given triangle the measure of two angles are 102 degree and 28 degrees and the sides of the triangle are a, 27 cm, c.

To find:

The value of a.

Solution:

Let the given triangle be ABC, such that,

$m\angle B=28^\circ$

$m\angle C=102^\circ$

$b=27\ cm$

Using angle sum property of triangles, we get

$m\angle A+m\angle B+m\angle C=180^\circ$

$m\angle A+28^\circ+102^\circ=180^\circ$

$m\angle A=180^\circ-28^\circ-102^\circ$

$m\angle A=50^\circ$

According to the Law of Sines:

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

$\dfrac{\sin 50^\circ }{a}=\dfrac{\sin 28^\circ }{27}$

$\dfrac{27\times \sin 50^\circ }{\sin 28^\circ}=a$

$\dfrac{27\times \sin 50^\circ }{\sin 28^\circ}=a$

$a\approx 44.06$

Therefore, the value of a is about 44.06 cm.