∆ABC in which AB=10cm,BC=11cm and angle B= 45°
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To find the missing side or angle of triangle ABC, we can use the Law of Cosines or the Law of Sines.
First, let's check if 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 the same for all sides and angles. The formula is:
a/sin(A) = b/sin(B) = c/sin(C)
In our triangle ABC, we know the lengths of sides AB and BC (a = 10cm, b = 11cm), and the measure of angle B (B = 45°). We are trying to find the missing side or angle, which we'll call x.
We can set up an equation using the Law of Sines:
x/sin(X) = 10/sin(45°) = 11/sin(C)
Now, let's solve for x:
x = (10 * sin(X)) / sin(45°)
To find the value of sin(X), we can rearrange the equation:
sin(X) = (x * sin(45°)) / 10
Now, we need to find the inverse sine (also known as arcsine) of the above ratio to get the value of angle X:
X = arcsin[(x * sin(45°)) / 10]
If you provide the value of angle C or the length of side AC, we can further simplify the equation to find angle X or side x.