Trig (I think) question (1 Viewer)

[Wonder]

The perpendicular height of an equilateral triangle is 12cm. Find the exact area of the triangle.

Please show all working. Thanks

 

[Shadowless]

Draw it out. It's really simple.

Essentially it's...

Let X = A side of the equilateral triangle.

Tan 60 = 12/x

x = 12/root3

Next part has two ways:
a) Area Triangle = 1/2 X Base X Height = 1/2 X 2x X 12
b) Area Triangle = 1/2 X A X B X Sin C = 1/2 X 2x X 2x X sin60

 

[Wonder]

Oh, right! Thank you!

 

[Shadowless]

Draw it out. It's really simple.

Essentially it's...

Let X = A side of the equilateral triangle.

Tan 60 = 12/x

x = 12/root3

Next part has two ways:
a) Area Triangle = 1/2 X Base X Height = 1/2 X 2x X 12
b) Area Triangle = 1/2 X A X B X Sin C = 1/2 X 2x X 2x X sin60

EDIT:

Tan 60 = 12/(x/2)

[If you draw it out you will see why.]