Question

Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).

Answer 1

Hello there. To solve this question, we'll have to remember some properties about triangles.

Given the triangle:

Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).

With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.

To find x, we'll have to apply the law of sines:

`(A)/(\sin(\alpha))=(B)/(\sin(\beta))=(C)/(\sin(\gamma))=2R`

In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:

`(x)/(\sin(73^(\circ)))=(4)/(\sin(85^(\circ)))`

Multiply both sides by a factor of sin(73º)

`x=(4\sin(73^(\circ)))/(\sin(85^(\circ)))`

Using a calculator, we get the following approximation (rounding to the nearest tenth):

`x\approx3.8`

This is the measure of x we're looking for.