Acute triangle

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

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:

$5²+8²=9²$

$25+64=81$

$89>81$

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:

$7²+7²=13²$

$49+49=169$

$169>98$

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.

$10.6≈\sqrt{113}$

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

$7²+8²=\sqrt{113}²$

$49+64=113$

$113=113$

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.

Let's look at 3 angles

Angle A is equal to $30°$

Angle B is equal to $60°$

Angle C is equal to $90°$

Task:

Can these angles form a triangle?

Solution:

$30+60+90=180$

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

therefore these angles can form a triangle.

Answer:

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

Angle A is equal to $90°$

Angle B is equal to $115°$

Angle C is equal to $35°$

Task:

Can these angles form a triangle?

Solution:

$90°+115°+35°=240°$

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

therefore these angles cannot form a triangle.

Answer:

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