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How do you find the angle opposite of the hypotenuse of a triangle with all three sides known?
Wiki User
∙ 14y ago
The only triangle that has a hypotenuse is a right-triangle. The hypotenuse is the side opposite the right angle, so the angle is always 90 degrees. In this case, if you're just finding the angle then you don't need to know what the side lengths are.
Wiki User
∙ 14y ago
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How are side angle side triangles and Hypotenuse leg alike?
"Hypotenuse-leg" is not necessarily the right-triangle version of "side-angle-side". It's the right-triangle version of "side-side-side", because if you know that it's a right triangle, and you know the hypotenuse and a leg, then you can calculate the length of the other leg. If you want to work with "side-angle-side", and you know the hypotenuse and a leg, then you can find the angle between them, because it's the angle whose cosine is (the known leg) divided by (the hypotenuse), and you can look it up.
Is the centroid of a triangle always the circumcenter of a triangle?
No way! An easy example is the centroid and circumcenter of a right-angle triangle. Circumcenter will be exactly on the middle of the hypotenuse which obviously cannot be the centroid. Centroid is the point where all three lines are connecting all the three vertices and the middle of the line opposite the respective vertex. Circumcenter is the center of the circle passing through all the vertices. As it is known, a right-angle triangle will always fall within a semicircle, meaning the circle center will always be on the middle of the hypotenuse.
How do you find the hypotenuse if you know one leg and one angle?
You need a bit more information to solve that one, because it's not clear whether the angle is opposite the leg you know or adjacent to it. If the angle is adjacent to the known leg, then divide the length of the leg by the cosine of the angle. If the angle is opposite the known leg, then divide its length by the sine of the angle.
What are the parts of a right triangle?
a right triangle has three sides like every triangle. A hypotenuse, which is the side opposite of the right angle, and the other two sides are known as legs. <-- that explains the sides pretty well. The angles are the right angle, of course, which is a perfect 90 degrees and two acute angles which is always going to be less than 90..i don't think there can be any other angles besides the acutes and right angle.
How do you find the length of one side if you have the others on a triangle?
If the triangle is a right triangle, where one angle is equal to 90o, Then you can use the Pythagorean Theorem. To use this, label each side of the right triangle a, b, and c, in which c is the hypotenuse/longest side/side opposite of the 90o angle; a2+b2=c2 . Just input the values into this equation and you are able to get one side as long as you know the other two. If the triangle is not a right triangle, then you would need to know an angle of one of the sides already known in order to use the law of cosines.
What can you say about the sides of a triangle opposite the largest angle?
The side of a triangle opposite the largest angle is the side of greatest length. It is also known as the Hypotenuse.
Can you find the hypotenuse of a right triangle when only one side length is known and all three angles?
Yes. You will need to use trigonometry. sin (angle) = opposite/hypotenuse cos (angle) = adjacent/hypotenuse tan (angle) = opposite/adjacent
Why is the sine of an angle less than 1?
In a right triangle, the sine of the angle is equal to the (leg opposite the angle) divided by the (hypotenuse). It's well known that the hypotenuse is always the longest side in the right triangle, so this division can never come out to be more than ' 1 '.
What is the hypotenuse angle theorem?
The hypotenuse angle theorem, also known as the HA theorem, states that 'if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.'
The law of cosine for angle are suited if are known?
In a right angle triangle if the lengths of the adjacent or the hypotenuse are known.
What is the relationship between the length of the legs of a 30-60-90 triangle?
-- The side opposite the 90° angle, known as the hypotenuse, is the longest of the three sides. The other two sides are called the "legs". -- The length of the leg opposite the 30° angle is 1/2 of the hypotenuse. -- The length of the leg opposite the 60° angle is 1/2 of the hypotenuse times sqrt(3). -- The sum of the squares of the lengths of the legs is the square of the length of the hypotenuse.
Why is sine used?
when trying to find the angle of a right triangle using only the opposite leg and the hypotenuse, eg. angle =sin opp leg over hyp * * * * * Also to find the area of a triangle if two sides and the included angle are known. Or the area of a sector of a circle.
What is one thing mentioned that Pythagoras is known for?
His theorem for a right angle triangle that states the hypotenuse of a right angle triangle when squared is equal to the sum of its squared sides.
How are side angle side triangles and Hypotenuse leg alike?
"Hypotenuse-leg" is not necessarily the right-triangle version of "side-angle-side". It's the right-triangle version of "side-side-side", because if you know that it's a right triangle, and you know the hypotenuse and a leg, then you can calculate the length of the other leg. If you want to work with "side-angle-side", and you know the hypotenuse and a leg, then you can find the angle between them, because it's the angle whose cosine is (the known leg) divided by (the hypotenuse), and you can look it up.
How do you find the other angles of a right triangle?
Using the mathematical principles of trigonometry, you will need to know the lengths of any two of the sides of the right-angled triangle in order to calculate the other angles. The ratios of the lengths can be looked up in tables (or a scientific calculator may be used) to find the angle. The three sides of a right angled triangle have names as follows:- Hypotenuse - the longest side of the triangle, opposite the right angle Adjacent - the side next to the angle you wish to know Opposite - the side opposite the angle you wish to know The ratios are named as follows:- Sine - ratio of length of Opposite divided by length of Hypotenuse Cosine - ratio of length of Adjacent dived by length of Hypotenuse Tangent - ratio of length of Opposite divided by length of Adjacent These can be remembered by the mnemonic SOH CAH TOA Depending on which sides have the known lengths, calculate the ratio and look up the value for the angle in the Sine, Cosine or Tangent table as applicable. Once the value for one angle is known, the value for the other angle is 90 minus the value of the known angle.
What is the Formula for finding the hypotenuse of a right triangle using trigonometric ratios?
In any triangle - not just right angled ones - the following holds true.* If angle A is opposite side a * and angle B is opposite side b * and angle C is opposite side cthen* SinAº/a = SinBº/b = SinCº/c (this is known as The Sine Rule)and* a2 = b2 + c2 − 2bc cosA (This is known as The Cosine Rule)So, all you ever need to know is three of the triangle's six properties and you can work out any of the others.
How do you find 2 missing sides of a right triangle?
Two methods to try . #1 Use pythagoras h^ = a^2 + a^2 NB THis is only good if you know that the two unknown sides are the same length. #2 Use trigonometry (trig.) This is good if you know the hypotenuse and one of the angles. Sine(angle) = opposite/ hypotenuse Hence opposite side = hypotenuse X sine(angle) Similarly Cosine(angle) = adjacent / hypotenuse. adjacent side = hypotenuse X Cosine(angle) Here is an example If you known the hypotenuse is a length of '6' and the angle is 30 degrees. Then opposite = 6 X Sin(30) opposite = 6 x 0.5 = 3 So the length of the oppisute sides is '3' units. NB DO NOT make the mistakes of saying Sin(6 X 30) = Sin(180) Nor 6 x 30 , nor Sin(6) X 30 , nor any other combination. You MUST find the SINE of the angle , then multiply it to the given length. Similarly for Cosine and Tangent.
