First, let's start by constructing the triangle (not scalable), like this:
Where b and h are the base and the height of the figure.
In order to determine the value of b and h we can use the following trigonometric function, the sine:

Where 17 is the length of the hypotenuse and a is the length of the side opposite to θ. From this formula, we can solve for a by multiplying by 17 on both sides to get:

As you can see, in the figure, the side opposite to the 60° angle is b, then by replacing 60 for θ and b for we get:

Then the value of b is calculated to get:

Similarly, we can get the value of h by replacing 30° for θ and h for a, like this:

Now we can use the following formula to calculate the area of the triangle:

By replacing 8.5 for h and 14.72 for b we get:

Then, the area of this triangle equals 62.57 square centimeters