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If two angles and the side opposite one of them in one triangle are equal to one side and two similarly located angles in a second triangle then the two triangles are congruent. (The triangles are exactly the same shape and size as each other).
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What are 15 facts about an equilateral triangle?
1. It has 3 sides. 2. It has 3 angles. 3. One is side a. 4. The angle opposite side a is Angle A. 5. The sceond side is side b. 6. The angle opposite side b is angle B. 7. The third side is side c. 8. The angle opposite side c is angle C. 9. All sides have equal lenght. 10. All angles have equal measures. 11. Each angle is 60 degrees. 12. The bisector of angle A will bisect side a. 13. The bisector of angle B will bisect side b. 14. The bisector of angle C will bisect side c. 15. Each bisector is perpendicular to the opposite side. 16. Each bisector creates a 30, 60, 90 right triangle.
How do you find the sides of a 30 60 and 90 degree triangle?
you cannot determine the sides of a triangle by the angle measures alone because any triangle with different side lengths can have these angle measurements. However if you do know the length of any one of the sides, you can calculate the lengths of the other two sides.The shortest side is the one opposite the 30 degree angle.The hypotenuse (opposite the 90 degree angle) is always twice the length of the shortest side opposite the 30 degree angle.The side opposite the 60 degree angle is always the length of the side opposite the 30 degree angle times the square root of three (about 1.73205).
How do you determine which is the adjacent side of a right triangle?
There are three sides, hypotenuse, opposite and adjacent. But the adjacent and opposite are not fixed sides: it depends on which of the two acute angles you are examining.For either of the non-right angles, the adjacent side is the one which forms the angle, along with the hypotenuse. For the given angle θ, the length of the adjacent side compared to the hypotenuse (adjacent/hypotenuse) is the cosine (cos θ).
How do you know that one of the sides of a right triangle is the hypotenuse?
It is opposite the right angle and it is the longest side.
A Angle formed by opposite ray is?
An angle cannot be formed by only one ray. However, an angle formed by two opposite rays is called a straight angle.
How do you find the length of one side of a triangle if only one side and two angles are given?
The sides and angles of a triangle are generally described using a,b,c for the three sides and A for the angle opposite side a, B for the angle opposite side b and C for the angle opposite side c. Then use the Sine Rule provided that one of the given angles is opposite the given side. a/Sin A = b/Sin B = c/Sin C
What does the side-angle inequality theorem state?
In a triangle, if one side is longer than the other side, the angle opposite the longer side is the larger angle. It state that If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.. I hope it will help in your study..... AJ
How do you find perimeter of triangle whose two sides are given?
You'll have to work out the length of the third side using:a) the sine rule (if information given has one side opposite a given angle and the unknown side also opposite a given angle)SIN RULE: sinA/a = sinB/b = sinC/cb) the cos rule (not opposite).COSINE RULE: a2 = b2 +c2 -2bc x CosA
If one angle of a triangle is larger than another angle then the side opposite the larger angle is?
the smaller side
What is the relationship among a right triangle?
There is the Pythagorean relationship between the side lengths. Given a right triangle with sides a, b, & c : Sides a & b are adjacent to the right angle, and side c is opposite the right angle, and this side is called the hypotenuse. Side c is always the longest side, and can be found by c2 = a2 + b2 The 2 angles (which are not the right angle) will add up to 90° Given one of those angles (call it A), then sin(A) = (opposite)/(hypotenuse) {which is the length of the side opposite of angle A, divided by the length of the hypotenuse} cos(A) = (adjacent)/(hypotenuse), and tan(A) = (opposite)/(adjacent).
What is a side-angle inequality?
If one side of a triangle is longer than the second side, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side. I hope it will help in your study.. AJ
What is the angle adjacent to a side equal to 23 feet and opposite a side equal to 14 feet of a right triangle?
Since the opposite side is not the longest one in the triangle, you're not describing the right angle. Knowing the lengths of the opposite side and the adjacent side of one of the acute angles allows us to immediately calculate the tangent of the angle. The tangent is (14/23) and the angle is 31.3 degrees. (rounded)
How do you fine the missing side of a right angle only given one side?
You need either two sides given, to find a third side. Or > you need one side and an angle, to find another side.
How do you find the third side of a triangle when the length of one side and one angle is known?
As stated knowing only 1 length and 1 angle, without further information with great difficulty; one angle and one side do not define a unique triangle. By saying "third side" I presume you know two of the sides, not just one as stated in the question, in which case you can use the cosine rule as long as the unknown side is opposite the angle: BC2 = AC2 + AB2 - 2 x AC x AB x cos A Other ways of finding sides from angles: If the triangle is a Right Angle triangle, you can use one of the trig functions Sin, Cos, Tan. If a second angle is given, all three angles can be known and the unknown sides can be calculated by the sine rule: sin A / BC = sin B / AC = sin C / AB If two sides are given and the given angle is opposite one of them, two applications of the sine Rule (first to find the angle opposite the second given side) will allow all angles and hence the third side to be found (by the second application).
What is the opposite side?
An "opposite side" depends on the shape that you have got. For a polygon with an even number of sides, (say 2n), the side which is opposite a given side is one that is nth from that side. In such a polygon a vertex does not have an opposite side. For a polygon with an odd number of sides, (say 2n+1), the side which is opposite a given vertex is one that is (n+1)th from that vertex. In such a polygon a side does not have an opposite side.
How do you find the length of the hypotenuse?
In a right-angled triangle, the hypotenuse is the longest side, opposite the right-angle. There are two ways of finding the length of the hypotenuse using mathematics: Pythagoras' theorem or trigonometry, but for both you need either two other lengths or an angle. For Pythagoras' theorem, you need the other two lengths. The theorem is a2+b2=c2, or the square root of the sum of two angles squared, where c=the hypotenuse. Let's say that one length is 4.8cm and the other 4cm. 4.82+42=6.22. So, the answer is 6.2cm. If you have one side and one angle, use trigonometry. You will need a calculator for this. Each side of the right-angled triangle has a name corresponding to the positioning of the angle given. The opposite is the side opposite the given angle, the adjacent is the side with the right-angle and the given angle on it, and the hypotenuse is the longest side or the side opposite the right-angle. There are three formulas in trigonometry: sin, cos and tan. Sin is the opposite/hypotenuse; cos is the adjacent/hypotenuse; and tan is the opposite/adjacent. As we are trying to find the hypotenuse, we already have either the opposite or the adjacent, and one angle. Let's say that our angle is 50o and we have the adjacent side, and that is 4cm. So, we have the adjacent and want to know the hypotenuse. The formula with both the adjacent and the hypotenuse in is cos. So, Cos(50o)=4/x where x=hypotenuse. We can single out the x by swapping it with the Cos(50o), so x=4/Cos(50o) -> x=6.22289530744164. This is the length of the hypotenuse, and is more accurate that Pythagoras' theorem.
What is the tangent of a triangle?
In that triangle, one of the angles must be a right angle, and another one of the angles must be marked with or the measurement of the angle. Tangent is the ratio of opposite side over adjacent side. The opposite and adjacent sides are determined by the position of the marked angle.
