Help. I have to angles and a side how do I do this Angle 1: 90 degrees Angle 2: 63 degrees Side 1: 5 mm
so I know angles need to add up to 180 so 90 +63=153 180-153=27 so the angle is 27
How do I figure out the sides? I have 5mm to start I am really confused.
the Law of Sines says that the length of the sides is the same ratio as the sines of the angles opposite the sides
angle 1 is 90º ... sine is 1
sin(angle 2) / 1 = side 2 / 5 mm
do the same with angle 3 and side 3
Not getting it how do you get 1 for 90 degrees and so on I am lost
To find the missing side length, you can use the Law of Sines or the Law of Cosines. Since you have two angles and one side, it is appropriate to 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. Mathematically, it can be expressed as:
(sine A) / a = (sine B) / b = (sine C) / c
In your case, you have angle 1 (90 degrees), its opposite side (side 1, 5 mm), and angle 2 (63 degrees) as given information. To find the length of the missing side, let's call it "b." We can set up an equation using the Law of Sines:
sin(angle 1) / side 1 = sin(angle 2) / b
Plugging in the values, we get:
sin(90°) / 5 mm = sin(63°) / b
Now, calculate the values of the sines:
1 / 5 mm = 0.891 / b
To solve for "b," we can cross-multiply:
1 * b = (5 mm) * 0.891
b = 4.455 mm
Therefore, the missing side length is approximately 4.455 mm using the Law of Sines.