Sydney is 8 miles far from the airplane if the plane took off at a 15° angle to the ground and flew in Sydney's direction option (A) 8 miles is correct.
Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
It is given that:
A plane took off at a 15° angle to the ground and flew in Sydney's direction.
She is standing at a point 25 miles from the point where the plane took off. If the plane has traveled 20 miles in the air
From the data we can draw a triangle:
From the diagram:
a + b = 25 miles
a = 20 cos(15)
h = 20 sin (15)
As we know, Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle that is equal to the sum of the squares of the other two sides.
Using Pythagoras theorem:
x = √(h² + b²)
x = √((20 sin15)² + (25 - 20 cos15)²)
After solving:
x = 7.68 miles
or
x = 8 miles
Thus, Sydney is 8 miles far from the airplane if the plane took off at a 15° angle to the ground and flew in Sydney's direction option (A) 8 miles is correct.
Learn more about trigonometry here:
brainly.com/question/26719838
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