the angles of an isosceles triangle are 66, 66, and 48. if the shortest side is 8.4 cm, find the length of one of the two equal sides

Question

this is a problem under our bearings topic. cant seem to understand how to get it done. thanks 

Answer 1

Hi Ash,

 

This is the same principle as the other problem except now you're given angles instead of sides.

 

Drop your perpendicular which bisects the bottom side leaving 4.2 cm as the adjacent side to one of the 66 degree angles. 

 

Cos 66 = adjacent / hypotenuse = 4.2 / X

 

Have fun.

 

Dan

Answer 2

Isosceles triangles have two congruent angles and two congruent sides.  We can use the laws of cosine to find the other two sides.

 

c² = a² + b² - 2abCos(C)

 

Side c is opposite to angle C.

 

If the shortest side is 8.4 cm , then the shortest angle must be 48 degrees.  The sides and angles are opposite to each other.

 

a = b     ---> congruent sides

c = 8.4

 

A = B   ---->  congruent angles

C = 48

 

8.4² = a² + a² - 2a²Cos(48)

 

8.4² = 2a² - 2a²Cos(48)

 

70.56 = 2a² - 2a²(0.669)

 

70.56 = 2a²(1 - 0.669)

 

213.172 = 2a²

 

106.586 = a²

 

10.32 = a

 

 

Since a=b, the other two sides are 10.32.