A is your angle.
sine(A) is equal to a/c.
cosine(A) is equal to b/c.
solve for a and b and you get:
a = c * sine (A)
b = c * cosine (A)
a is the height of your triangle.
b is the base of your triangle.
the area of the triangle is equal to 1/2 * base * height which becomes:
area of the triangle is equal to 1/2 * b * a which becomes:
area of the triangle is equal to 1/2 * c * cosine (A) * c * sine (A).
this can be simplified to:
area of the triangle is equal to 1/2 * c^2 * cosine (A) * sine (A).
replace c with 5 and replace A with pi/10 and you get:
area of the triangle is equal to 1/2 * 5^2 * cosine (pi/10) * sine (pi/10).
use your calculator to find sine and cosine (pi/10). the angle should be in radians. if you want to work in degrees, then convert angle in radians to angle in degrees by multiplying the angle in radians by 180 / pi. you will get pi/10 * 180 / pi = 18 degrees.
anyway, regardless of whether you are working in degrees or radians, you will get:
area of the triangle is equal to 1/2 * 25 * .951056516 * .309016994 which is equal to 3.673657827 which you can round to 3.67
