Find the Value of X in simplest radical form and Find the measure of angle A.
1 answer:
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;
∠A = arcsine (1/2) = 30°
Angle A = 30°
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Hi!
We are given the information found in the picture below.
Note: The directions aren't correct, but the triangle works for this problem.
The "direct path" is the hypotenuse of this triangle.
To find this, we use the Pythagorean Theorem, where and
are 2 legs of the triangle, and
is the hypotenuse, aka the longest side of any triangle:
We know and
and want
Therefore, is approximately
