Find the area of this triangle..

[#1procrastinator]

...using the sine formula

This is from the Essentials textbook, Ch. 13, I think section D and question 1d



I've tried changing around the the numbers and all that but nothing gives the given answer

[kenhung123]

LOOOOOOOOOOOL how did you draw that??
Use sin rule to find other side then you can use Herons

[brightsky]

no need to use heron's formula, it's an isosceles triangle so just find the altitude (which would be 5sin(15)), then multiply this by the base length (5sin(150)/sin(15)) and then halve it.

[JinXi]

Edit : Accident Double posted

[JinXi]

Since it's an isocelles triangle, 2 of the edges have a angle of 15 degree.

The 3rd angle between then 2 side lengths of 5 would be 150 degrees.

so, use the triangle formula. 0.5*(5)*(5)*sin(150)

Edit: Not sure if this method is valid for *Using the sine formula?

[kenhung123]

As an alternative method 

[#1procrastinator]

Thanks, but is it possible to use the sine formula (just curious)? (it doesn't say you have to use the sine formula by the way, but I assumed you should based on the examples)

[BubbleWrapMan]

Since it's isosceles you can easily calculate the other two angles. The other base angle is also 15º which means the angle enclosed by the two equal sides is 150º. So the area is given by:

1/2 x 5 x 5 x sin(150º)