please help geometry!

Question

Find the area of the sector of the disk of radius

r = 13 and with arc length s = 17.

Consider the isosceles triangle

4 inches

50 ◦

50 ◦

Find the altitude.

Answer in units of inches.

Answer 1

Drop altitude from vertex of isosceles triangle to base, dividing base into equal lengths of 2.

Now have right triangle with hypotenuse 50 and base 2.

Altitude is other leg of right triangle = sqrt(50^2 - 4^2).

s = r * central angle in radians

17 = 13 * central angle in radians

17/13 = central angle

area = 1/2 * radius^2 * central angle