Answer:
Step-by-step explanation:
The angle bisector of a triangle divides the opposite side in 2 segments that are proportional to the other 2 sides of the triangle. Namely:
and cross multiply.
18w = 450 so
w = 25
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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