Answer:
A = 30°
x = 9·√3
Step-by-step explanation:
Part A
In the drawing, we are given;
The radius of the circle with center at point S = SA = 18
ΔAHA is a right triangle
One of the leg length of ΔASH = 9
The length of the hypotenuse side of ΔASH, AS = 18 The radius of the circle with center at the point 'S'
By Pythagoras's theorem, the length of the (radius) side, AS = √(SH² + AH²)
∴ AH = √(AS² - SH²)
AH = √(18² - 9²) = √(243) = 9·√3
AH = 9·√3
By circle theorem, SH bisects the line AH extended to the circumference of the circle
SH bisects the line with length AH + x
∴ AH = x
x = AH = 9·√3
x = 9·√3
Part B
By trigonometric ratios, we have;
[tex]sin\angle A = \dfrac{Opposite \ leg \ length}{Hypotenuse \ length}[/tex]
[tex]\therefore sin\angle A = \dfrac{9}{18} = \dfrac{1}{2}[/tex]
∠A = arcsine (1/2) = 30°
Angle A = 30°
