given sides lenghts 7, 6 and 6?

Question

which one?
a right
a obtuse
a acute
or not a right triangle
explain please

Answer 1

If the largest angle can be either obtuse, right angled or acute. The other two angles will always be acute, as a triangle can have at most one obtuse angle or one right angle and at least two acute angles

So only one angle needs be investigated and that is the largest angle which is found opposite the largest side.

It is not rightangled as 7² ≠6² + 6²

Let it be A and the other two angles be B and C

So by the cosine rule

cos A = (b² + c² - a²)/(2bc)

So in this case:

cos A = (6² + 6² - 7²)/ (2*6*6) >0

So A is acute

Therefore the triangle is an acute angled (isosceles) triangle

(You could have just about gambled on this as the triangle is almost equilateral)

In fact:

if the sum of the squares of the two shorter sides > square of the longer side the triangle is acute angled (as cos A > 0)

if the sum of the squares of the two shorter sides = square of the longer side the triangle is right angled (as cosA = 0)

if the sum of the squares of the two shorter sides < square of the longer side the triangle is obtuse angled (as cosA < 0)

Answer 2

First, for the shape to exist, the sums of any two sides cannot be smaller than the third side.
6+7 > 6
6+6 > 7
7+ 6 > 6

We're good -- the figure is definitely a triangle.

For it to be a right triangle, the sides would have to satisfy this equation: a^2 + b^2 = c^2 where c is the longest side.

6^2 + 6^2 =? 7^2
36 +36 =? 49
72 does not equal 49. The triangle is not right. If the sums of the squares of the two sides is smaller than the square of the longest side, then the triangle is acute. As this is the case, 72>49, we can say that the triangle is acute.

Answer 3

To determine which type of triangle a triangle
C= Hypotenuse=longest side
A^2 + B^2 = C^2, then it's Right
A^2 + B^2 is less than C^2 then it's Obtuse
A^2 + B^2 is greater than C^2 then it's Acute
thus 6^2 + 6^2 ? 7^2
since 72 is greater than 49, it's an acute triangle

Answer 4

The triangle is acute (also isosceles, as the other poster says) because the 6^2 + 6^2 > 7^2.

Answer 5

It is an acute triangle. All three of the angles are less than 90°.
It is also not a right triangle.

To be precise, it is an isosceles acute triangle. Work out the angles of the triangle to verify using the law of cosines.

a² = b² + c² - 2bc cos A

Answer 6

On a triangle, the hypotenuse would desire to be shorter than the two legs of the triangle further together. the reason is going without postpone would desire to be shorter than taking a various direction. to classify the triangle use the Pythagorean concept to aim it. so for: a million. take longest side (6) and ensure that because of the fact the hypotenuse. upload the two different sides that are the legs (2+5=7). 7 is better than 6 for this reason it incredibly is a triangle. 2. comparable factor. 6.5 as hypotenuse, 5.4+3.8=9.2, 9.2 > 6.5, for this reason it incredibly is a triangle. 15. 7 hypotenuse, 7+2=9, 9 > 7, for this reason it incredibly is a triangle

Answer 7

not a right triangle. because for that 7^2 = 6^2 + 6^2 which is not equal.

Answer 8

isoceles triangle

not a right triangle as 7^2 =/= 6^2 + 6^2

Answer 9

Use the law of cosines
7^2=6^2+6^2-2*6*6*cos b
49=2*36-2*36*cos b
49-72=-72 cos b
cos b=(72/49)/23
b=arccos 23/72
b=71.4°
it is an acute triangle. the other 2 angles are
a=(180°-71.4°)/2=54.3°

Answer 10

Acute. All the angles are less than 90 degrees.

You can prove this with trig or by construction.