## Definition of Acute Triangle

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

## Examples with solutions for Acute triangle

### Exercise #1

Is the triangle in the drawing a right triangle?

### Step-by-Step Solution

Since we see the symbol that represents an angle equal to 90 degrees, indeed this is a right-angled triangle.

Yes

### Exercise #2

Is the triangle in the drawing a right triangle?

### Step-by-Step Solution

It can be seen that all angles in the given triangle are less than 90 degrees.

In a right-angled triangle, there needs to be one angle that equals 90 degrees

Since this condition is not met, the triangle is not a right-angled triangle.

No

### Exercise #3

Given the values of the sides of a triangle, is it a triangle with different sides?

### Step-by-Step Solution

As is known, a scalene triangle is a triangle in which each side has a different length.

According to the given information, this is indeed a triangle where each side has a different length.

Yes

### Exercise #4

In a right triangle, the sum of the two non-right angles is...?

### Step-by-Step Solution

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

$90+90=180$

90 degrees

### Exercise #5

Calculate the size of angle X given that the triangle is equilateral.

### Step-by-Step Solution

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

60

### Exercise #6

What kid of triangle is the following

### 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°,

$C=107$

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

$107+34+39=180$

The triangle is obtuse.

Obtuse Triangle

### Exercise #7

What kid of triangle is given in the drawing?

### Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Right triangle

### Exercise #8

What kind of triangle is given in the drawing?

### 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°:

$70+70+40=180$

The triangle is isosceles.

Isosceles triangle

### Exercise #9

Which kind of triangle is given in the drawing?

### 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.

Equilateral triangle

### Exercise #10

What kind of triangle is given in the drawing?

### 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.

Isosceles triangle

### Exercise #11

What kind of triangle is given here?

### Step-by-Step Solution

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

Scalene triangle

### Exercise #12

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

### Step-by-Step Solution

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

### Exercise #13

Can a triangle have more than one obtuse angle?

### Step-by-Step Solution

If we try to draw two obtuse angles and connect them to form a triangle (i.e., only 3 sides), we will see that it is not possible.

No

### Exercise #14

Look at the isosceles triangle below:

What is its perimeter?

### Step-by-Step Solution

Since we are referring to an isosceles triangle, the two legs are equal to each other.

In the drawing, they give us the base which is equal to 4 and one side is equal to 6, therefore the other side is also equal to 6.

The perimeter of the triangle is equal to the sum of the sides and therefore:

$6+6+4=12+4=16$

16

### Exercise #15

The two legs of the triangle are equal. Calculate the perimeter of the triangle.

### Step-by-Step Solution

Since the two legs are equal, we can claim that:

$AB=AC=9$

The perimeter of the triangle is equal to the sum of all sides, meaning:

$AB+AC+BC$

Let's substitute the known data and calculate the perimeter:

$9+9+3=18+3=21$