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Hanley Rd, Suite St. Louis, MO Subject optional. Email address: Your name:. Possible Answers:. Correct answer:. Explanation : By the Triangle Inequality, the sum of the lengths of two shortest sides must exceed that of the third. Then Case 2: is not the greatest of the three sidelengths - that is, 11 is. Report an Error. Explanation : If two sides are 4 and 8, then the third side must be greater than and less than.
Which of the following is true of a triangle with sides that measure 15, 17, and 21? Possible Answers: It is a right triangle. None of these statements can be proved without further information. Correct answer: It is an acute triangle. Explanation : The triangle can exist by the Triangle Inequality, since the sum of the two smaller sides exceeds the greatest: To determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side.
Since this sum is greater, the triangle is acute. Possible Answers: The triangle is isosceles and acute. Correct answer: The triangle is scalene and obtuse. Explanation : If these are the measures of the interior angles of a triangle, then they total. One angle measures The others measure: Since the largest angle measures greater than , the angle is obtuse, and the triangle is as well. None of the other responses gives a correct answer. Explanation : The three sides of a scalene triangle have different measures, so 15 can be eliminated.
Correct answer: This triangle cannot exist. Explanation : By trial and error, we get four ways to add distinct primes to yield sum In each case, however the Triangle Inequality is violated - the sum of the two shortest lengths does not exceed the third.
No triangle can exist as described. Explanation : A scalene triangle has three sides of different lengths, so we are looking for three distinct prime integers whose sum is a prime integer.
Therefore, beginning with the least three odd primes, add increasing triples of distinct prime numbers, as follows, until a solution presents itself: - incorrect - correct The correct answer, 19, presents itself quickly. Explanation : A scalene triangle has three sides of different lengths, so we are looking for three distinct prime integers whose sum is There are ten ways to add three distinct primes to yield sum By the Triangle Inequality, the sum of the lengths of the shortest two sides must exceed that of the greatest.
Circumcenter H , the median point from all the triangle vertices, lies outside in an obtuse triangle. Example 1: Which of the following angle measures can form an obtuse-angled triangle? Among the given options, option b satisfies the condition. Therefore, option b i. Therefore, the height of the obtuse triangle can be calculated by:. Example 3: Can sides measuring 3 inches, 4 inches, and 6 inches form an obtuse triangle?
The sides of an obtuse triangle should satisfy the condition that the sum of the squares of any two sides is lesser than the square of the third side. The given measures can form the sides of an obtuse triangle. Therefore, 3 inches, 4 inches, and 6 inches can be the sides of an obtuse triangle. It has one of its vertex angles as obtuse and other angles as acute angles i.
An obtuse triangle can also be called an obtuse-angled triangle. In general, an obtuse triangle can be a scalene triangle or isosceles triangle but not an equilateral triangle.
The circumcenter and orthocenter lie outside the triangle while the centroid and incenter come inside the obtuse triangle. The longest side of a triangle is considered to be the opposite side of the obtuse angle. To find if a triangle is obtuse, we can look at the angles mentioned. Learn Practice Download. Obtuse Triangle An obtuse triangle is a triangle with one interior angle measure greater than 90 degrees.
What Is an Obtuse Triangle? Obtuse Angled Triangle Formula 3. Obtuse Angled Triangle Properties 4. We can prove this by contradiction. This is a contradiction. Therefore, our assumption must be wrong. Example 1: Check whether a triangle with side lengths 6 cm, 10 cm, and 8 cm is a right triangle. A corollary to the theorem categorizes triangles in to acute, right, or obtuse.
Example 2: Check whether the triangle with the side lengths 5 , 7 , and 9 units is an acute, right, or obtuse triangle. The longest side of the triangle has a length of 9 units. Subjects Near Me.
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