Acute triangle

🏆Practice types of triangles

Definition of Acute Triangle

An acute triangle has all acute angles, meaning each of its three angles measures less than 90° 90° degrees and the sum of all three together equals 180° 180° degrees. 

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In a right triangle, the side opposite the right angle is called....?

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Next, we will look at some examples of acute triangles:

Acute triangle

A1 - acute triangle

3 Examples of acute triangles

3 Examples of acute triangles


Exercises with Acute Triangles

Exercise 1

Determine which of the following triangles is obtuse, which is acute, and which is a right triangle

Assignment:

Determine which of the following triangles is obtuse, which is acute, and which is a right triangle:

Solution:

A. We will examine if the Pythagorean theorem holds for this triangle:

52+82=92 5²+8²=9²

25+64=81 25+64=81

89>81 89>81

The sum of the squares of the perpendicular sides is greater than the square of the remaining side, therefore it is an acute-angled triangle.

B. Now we will examine this triangle:

72+72=132 7²+7²=13²

49+49=169 49+49=169

169>98 169>98

The sum of the squares of the perpendicular sides is greater than the square of the remaining side, therefore it is an obtuse-angled triangle.

10.6≈113 10.6≈\sqrt{113}

C. The longest side of the 3 will be treated as the hypotenuse.

72+82=1132 7²+8²=\sqrt{113}²

49+64=113 49+64=113

113=113 113=113

The Pythagorean theorem holds true and therefore triangle 3 is a right triangle.

Answer:

A-acute angle acute B-obtuse angle obtuse C-right angle right.


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Exercise 2

Let's look at 3 angles

Angle A is equal to 30° 30°

Angle B is equal to 60° 60°

Angle C is equal to 90° 90°

Task:

Can these angles form a triangle?

Solution:

30+60+90=180 30+60+90=180

The sum of the angles in a triangle is equal to 180° 180° ,

therefore these angles can form a triangle.

Answer:

Yes, since the sum of the internal angles of a triangle is equal to 180° 180° .


Exercise 3

Angle A is equal to 90° 90°

Angle B is equal to 115° 115°

Angle C is equal to 35° 35°

Task:

Can these angles form a triangle?

Solution:

90°+115°+35°=240° 90°+115°+35°=240°

The sum of the angles is greater than 180° 180° ,

therefore these angles cannot form a triangle.

Answer:

No, since the sum of the internal angles must be 180° 180° , and in this case the angles add up to 240° 240° .


Examples and exercises with solutions for acute triangles

Exercise #1

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #2

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer

Equilateral triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer

Isosceles triangle

Exercise #5

What kind of triangle is given here?

111111555AAABBBCCC5.5

Video Solution

Step-by-Step Solution

Since none of the sides have the same length, it is a scalene triangle.

Answer

Scalene triangle

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