What is the measure of angle A to the nearest degree?
1 answer:
There are several ways to find the angle at A.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.
One is to realize the bisector of angle A will make a right angle with BC, creating two congruent triangles with short leg 2 and hypotenuse 7. Then the sine of the half-angle at A will be 2/7, so
A = 2*arcsin(2/7)
A ≈ 2*16.6015° = 33.203°
The measure of the angle at A to the nearest degree is
33°
_____
Another way to find the angle is to use the Law of Cosines. After solving for the angle (A) in terms of sides a, b, c, you find
A = arccos((b²+c²-a²)/(2bc)) = arccos(7²+7²-4²)/(2*7*7))
A = arccos(82/98) ≈ 33°
And you can always use a triangle solver application.
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So the order of transformation that is happening to f(x) = x³ is translation four units to the right, half the y-coordinate, then translate 5 units up.
Notice the function f(x) = (x - 4)³ that a value '4' is subtracted from 'x' ⇒ This means the function f(x) is translated four units to the right.
Then the function f(x) = ¹/₂ (x - 4)³, the function (x - 4)³ is halved vertically ⇒ Half the y-coordinate
Then the function f(x) = ¹/₂ (x - 4)³ + 5 that a value '5' is added to ¹/₂ (x - 4)³ ⇒ This means the function f(x) is translated five units up
So the order of transformation that is happening to f(x) = x³ is translation four units to the right, half the y-coordinate, then translate 5 units up.