Question

two angles of a triangle measure 59° and 63°. if the longest side measures 28 cm find the length of the shortest side. round answers to the nearest tenth

Answer 1

The two angles of triangle are : 59 and 63 degrees.

Length of the longest side of traingle is 28cm.

In a triangle,

the smallest side is always opposite to the smallest angle of the triangle,

and the largest side is always opposite to the largest angle

The sum of all the angles in atriangle is 180 degree

let the other angle is x so,

x+63+59=180

x=180-59-63

x=58

So, the longest side of traingle is in the opposite of angle 63

the smallest side of triangle is in opposite of angle 58

Apply the Sine rule to find the side of the traingle which has an opposite angle of 58.

Sine formula is expressed as:

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

Let a be the smallest side and b be the longest side of triangle so,

A=58, B=63, b=28cm

Substitute the values, and solve for a,

The shortest length is 26.7cm