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The Sine Rule is
SinA/a = SinB /b = SinC/c
For any given triangle, where two sides and one angle are known, use the Sine Rule
If the two sides are 'a' & 'b' , and Angle 'B' is known then, initially ignore the C/c compoentne.
So it reduces to
SinA/a = SinB/b
To find SinA
Then
SinA = aSinB/b
For example if Angle B = 30 degrees , 'a' = 3 & 'b' = 5
Then substituting
SinA = 3Sin30/ 5
First find the Sine of 30 , which is 0.5
Hence
SinA = 3*0.5/5
SinA = 1.5/5
SinA = 0.3
Hence
A = Sin^(-1) 0.3 (or ArcSin(0.3)) = 17.457.... degrees.
NB Select any two terms from 'A/a' B/b , or C/c'. Do NOT try to use all three in one calculation.
NNB Sometimes the Sine Rule is written as
a/SinA = b/SinB = c/SinC
However, it works just the same.
Hope that helps!!!!!
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How do you find an angle measurement of a triangle?
The answer depends on what information you have, If you know only the lengths of the sides, you use the cosine rule to find the measure of one angle and then the sine rule to find the other angles.
A ski slope is 250 yards long with a vertical drop of 100 yardsfind the angle of depression of the slope?
The angle of depression is equal to the angle of elevation, so use the sine ratio to find the angle. sine = opposite (the vertical drop) divided by the hypotenuse (the ski slope) sine = 100/250 = 2/5 or 0.4 sine-1(0.4) = 23.57817848 degrees which is about 24 degrees
How do you find the perpendicular distance in a triangle?
The answer will depend on what information you do have.If you know two sides and the included angle you can find the area. Then perpendicular distance = 2*Area/Base.If you know all three sides then you can use the cosine rule to find one of the angles. Then, you have two sides and the included angle and can proceed as above. Actually, you can find the area directly from the three sides.If you know one side and two angles, you effectively know one side and all three angles. You can use the sine rule to find one of the other sides and then you have two sides and an included angle and so can proceed as before.There are more complicated solutions where other measures are known.The answer will depend on what information you do have.If you know two sides and the included angle you can find the area. Then perpendicular distance = 2*Area/Base.If you know all three sides then you can use the cosine rule to find one of the angles. Then, you have two sides and the included angle and can proceed as above. Actually, you can find the area directly from the three sides.If you know one side and two angles, you effectively know one side and all three angles. You can use the sine rule to find one of the other sides and then you have two sides and an included angle and so can proceed as before.There are more complicated solutions where other measures are known.The answer will depend on what information you do have.If you know two sides and the included angle you can find the area. Then perpendicular distance = 2*Area/Base.If you know all three sides then you can use the cosine rule to find one of the angles. Then, you have two sides and the included angle and can proceed as above. Actually, you can find the area directly from the three sides.If you know one side and two angles, you effectively know one side and all three angles. You can use the sine rule to find one of the other sides and then you have two sides and an included angle and so can proceed as before.There are more complicated solutions where other measures are known.The answer will depend on what information you do have.If you know two sides and the included angle you can find the area. Then perpendicular distance = 2*Area/Base.If you know all three sides then you can use the cosine rule to find one of the angles. Then, you have two sides and the included angle and can proceed as above. Actually, you can find the area directly from the three sides.If you know one side and two angles, you effectively know one side and all three angles. You can use the sine rule to find one of the other sides and then you have two sides and an included angle and so can proceed as before.There are more complicated solutions where other measures are known.
If this is opposite is 30 degree angle in a right triangle is 12.5 meters how long is the hypotenuse rounding to the nearest tenth?
If the angle opposite the side of 12.5 meters is 30 degrees then use the sine ratio to find the hypotenuse which works out as 25.0 meters.
You know base and angles how do I find height of isosceles triangle?
Use the sine rule to work out one of the sides. (a/sina = b/sinb = c/sinc) Then as it is an isosceles triangle the perpendicular dropped from the apex will (a) bisect the base and (b) form a right angle with the base. Now you know one side and the hypotenuse of a right-angled triangle and you use Pythagoras (a2 + b2 = c2) to solve the 'other' side of that, which is the height of the isosceles triangle.
How do you find an angle measurement of a triangle?
The answer depends on what information you have, If you know only the lengths of the sides, you use the cosine rule to find the measure of one angle and then the sine rule to find the other angles.
Is it is necessary to be a right angle triangle to use sine rule?
No. Sine rule (and cosine rule) apply to all triangles in Euclidean space (plane geometry). A simplification occurs when there is a right angle because the sine of the right angle is 1 and the cosine is 0. Thus you get Pythagoras theorem for right triangles.
How do you work out the inside angle of a triangle using trigonometry?
The answer depends on what information you do have. If you have all three sides, you use the cosine rule to find any one of the angles and then use the sine rule to find the other two.
What ratio do you use to find the sine of an angle in a right triangle?
Sine ratio = opposite/hypotenuse
How do you work out the angle of an iscoseles triangle using the sine rule only having two lengths?
The sine rule involves ratios of lengths to angles; given only two lengths, I cannot see how it is possible to use the sine rule.You can, however, use the cosine rule to find an angle provided that you can know all three lengths.If you have been given one of the two equal lengths (and know which of the lengths you have been given it is) and the other length you will know all three lengths. The you can use the cosine rule to find one of the angles:a2 = b2 + c2 - 2bc cos Awhere in triangle ABC, a is opposite angle A (that is side BC), b is opposite angle B (side AC) and c is opposite angle C (side AB).Once one angle has been found you can then either use the cosine rule with a different angle, the sine rule as you now know one angle, or make use of the fact that the sum of the angles of a triangle is 180o and that two of the angles are equal (and that you now either know one of them or the other angle - depending upon which one you calculated).
How do you find a measurement of an angle in a triangle when you only know the side length?
If you do not know only a side length you cannot. If you know all three side lengths then you can use the cosine rule. You can continue using the cosine rule for the other two angles but, once you have one angle, it is simpler to use the sine rule.
How do you work out missing angles in a triangle?
The 'best' conditions for doing this is when you have two angles... add them together and the difference between their total and 180 degrees is the magnitude of the remaining angle. Otherwise, if you have one angle and the lengths of two sides you can use the sine rule. This states that the length of each side, divided by the sine of the angle opposite it, is equal to the length of any other side, divided by the sine of the angle opposite it - or..... a/sin A = b/sin B = c/sin C Or, if you don't have a matching angle and side, you can use the cosine rule. This says that a2 = b2 + c2 - 2bc cosA Now you have an angle and the side opposite it, and you can use the sine rule above.
How do you find the missing length of a triangle?
You use the Pythagoras Theorem if it is a right-angled triangle. a squared + b squared = h (longest side, diagonal) squared, then square root h to find the longest side. if it is not a right angled triangle, then use the Sine or Cosine rule. Sine rule for: two angles and any one side or two sides and an angle that is not in between the sides. Cosine rule for: all three sides (but then you do not need to find a missing side) or two sides and an angle that is in between.
How can i find out the hypotenuse if i only have 1 side and an angle?
Use the appropriate sine or cosine ratio.
How do you find the diameter of a cone base given the side lengths and the angle degree?
The answer depends on which angle is given: whether it is the angle made by the sloping face with the base, or the angle at the apex or even the angle that the sloping face makes with the vertical. Essentially, though, you use Pythagoras's theorem or, equivalently, the sine rule.
What is midpointHow do you find the length of the third side of an scalene triangle?
If you have angles, use the sine rule: a/sin A = b/sin B = c/sin C a denotes the side, A the angle opposite the side.
What proportion do you use to find the length of the third side triangle XYZ?
The answer depends on the information that you have: it could be the sine rule or the cosine rule.
