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


Exercises with Acute Triangles

Exercise 1

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.

10.6113 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° .


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