In ΔABC, angleB = 46°, angleC = 28° and AB = 50. Find BC (to the nearest hundredth).
To find BC in triangle ABC, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides of the triangle.
Let's label the angles and sides:
angle A = 180° - angle B - angle C (since the sum of the angles in a triangle is 180°)
angle A = 180° - 46° - 28°
angle A = 106°
Using the Law of Sines, we have:
BC / sin(B) = AB / sin(A)
Substituting the values we know:
BC / sin(46°) = 50 / sin(106°)
Now, we can solve for BC:
BC = (50 * sin(46°)) / sin(106°)
Using a calculator, we find:
BC ≈ 36.60 (rounded to the nearest hundredth)
Therefore, BC is approximately 36.60.
To find the length of side BC in triangle ABC, we can use the law of sines. The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we can set up the following equation using the law of sines:
sin(angleB) / AB = sin(angleC) / BC
Plugging in the given values:
sin(46°) / 50 = sin(28°) / BC
Let's solve for BC:
First, find the value of sin(46°):
sin(46°) ≈ 0.71934
Now, substitute the known values into the equation and solve for BC:
0.71934 / 50 = sin(28°) / BC
Cross-multiply to isolate BC:
BC * 0.71934 = 50 * sin(28°)
BC ≈ (50 * sin(28°)) / 0.71934
Using a calculator, evaluate sin(28°):
sin(28°) ≈ 0.46947
Now, substitute this value into the equation:
BC ≈ (50 * 0.46947) / 0.71934
BC ≈ 32.9332
Therefore, the length of side BC is approximately 32.93 (rounded to the nearest hundredth).
easy to find angle A
angle A = 180-28-46 = 106
now sine law:
BC / sin 106 = 50/sin 28
BC = ....