Answer:
f = 53.13 degrees
Explanation:
An isosceles triangle has two equal sides, so in this case the sides of length 60cm are equal. The base angle (f) is opposite the base of the triangle, which is the side of length 100cm.
To find the base angle, we can use the law of cosines.
c^2 = a^2 + b^2 - 2ab*cos(f)
where c is the hypotenuse (the side of length 100cm), a and b are the legs (the sides of length 60cm), and f is the base angle we are trying to find.
Substituting in the given values, we get:
100^2 = 60^2 + 60^2 - 2(60)(60)cos(f)
Simplifying this equation, we get:
10000 = 3600 - 3600cos(f)
so
cos(f) = (10000-3600)/3600 = 6400/3600 = (8/3)^2
then
f = cos^-1((8/3)^2)
Therefore, f = 53.13 degrees