Given the perimeter of the triangle △ADC equal to 30 cm.
From here we can calculate AD.
AD+DC+AD=PerimeterΔADC
AD+5+13=30
AD+18=30 /−18
AD=12
Now we can calculate the area of the triangle ΔABC
Pay attention: we are talking about an obtuse triangle therefore its height is AD.
We use the formula to calculate the area of the triangle:
2sideheight×side=
2AD⋅BC=212⋅4=248=24
Answer:
The area of the triangle ΔABC is equal to 24 cm².
Exercise 6
Homework:
Given the right triangle ΔABC
The area of the triangle is equal to 38 cm², AC=8
Find the measure of the leg BC
Solution:
We will calculate the length of BC using the formula for calculating the area of a right triangle:
2leg×leg
2AC⋅BC=28⋅BC=38
Multiply the equation by the common denominator
/ ×2
Then divide the equation by the coefficient of BC
8×BC=76 /:8
BC=9.5
Answer:
The length of the leg BC is equal to 9.5 centimeters.
Do you think you will be able to solve it?
Question 1
Look at the angle shown below and choose the correct statement.
Incorrect
Correct Answer:
All answers are incorrect.
Question 2
right angle?
Incorrect
Correct Answer:
Angle of 90°.
Question 3
What is a flat angle?
Incorrect
Correct Answer:
Angle of 180°.
Exercise 7
In front of you, there is a right triangle ΔABC.
Given that BC=6 The length of the leg AB is greater by 3331% than the length of BD.
The area of the triangle ΔADC is greater by 25 than the area of the triangle ΔABD.
Task:
What is the area of the triangle ΔABC?
Solution:
To find the measure of the leg AB we will use the data that its length is greater by 33.33 than the length of BD.
AB=1.33333⋅BD
(100100+10033.33=100133.33=1.333)
AB=1.333⋅6=8
Now we will calculate the area of the triangle ΔABD.
SΔABD=2AB⋅BD=28⋅6=248=24
Answer:
24 cm².
Exercise 8
Homework:
What data in the graph is incorrect?
For the area of the triangle to be 24 cm², what is the data that should replace the error?
Solution:
Explanation: area of the right triangle.
SΔEDF=2ED⋅EF=28⋅6=248=24
According to the formula:
2leg×leg
If the area of the triangle can also be calculated from the formula of:
2side×heightofside
2EG×10=24 /×2
10EG=48 /:10
EG=4.8
Answer:
The incorrect data is EG.
The length of EG should be 4.8 cm.
Test your knowledge
Question 1
True or false?
An acute angle is smaller than a right angle.
Incorrect
Correct Answer:
True
Question 2
Is a plane angle greater than an obtuse angle?
Incorrect
Correct Answer:
True
Question 3
\( ∢\text{ABC} \) equal to 90°.
What angle is it?
Incorrect
Correct Answer:
Right angle
Exercise 9
In the following example, a square ABCD is presented.
A. Is the angle ∡ABC equal to the angle of ∡ADC? Can it be said that BD serves as the bisector of the angle ∡ABC?
Bisector inside a square
Solution to exercise 2:
The line BD created 2 points where the angle was divided into 2 equal angles.
Answer:
Therefore, DB is a bisector of the two angles ∡ADC and ∡ABC
Do you know what the answer is?
Question 1
What type of angle is
\( ∢\text{ABC} \) ?
Incorrect
Correct Answer:
Flat angle
Question 2
\( ∢\text{ABC} \) is an angle measuring less than 90°.
What kind of angle angle is it?
Incorrect
Correct Answer:
Acute angle
Question 3
Which figure depicts a right angle?
Incorrect
Correct Answer:
Examples with solutions for Right angle
Exercise #1
∢ABC equal to 90°.
What angle is it?
Step-by-Step Solution
To solve this problem, we'll follow these steps:
Step 1: Identify the angle measure provided.
Step 2: Match the angle measure to the corresponding type of angle.
Step 3: Choose the correct type of angle from the multiple-choice options.
Let's break down the process:
Step 1: The problem specifies that ∠ABC=90∘.
Step 2: Recall the definitions of angle types. A right angle is defined as an angle that measures exactly 90 degrees.
Step 3: Out of the provided choices, select the one that represents a right angle.
- Right angle: ∠=90∘ (Correct Choice)
- Acute angle: ∠<90∘
- Obtuse angle: ∠>90∘ and ∠<180∘
- Flat angle: ∠=180∘
Thus, the conclusion is that ∠ABC is a Right angle.
Answer
Right angle
Exercise #2
What type of angle is
∢ABC ?
Step-by-Step Solution
To determine the type of angle ∠ABC, we will consider the following:
Step 1: Observe the positions of points A, B, and C, which are depicted in the diagram as lying on a straight line.
Step 2: Recognize that when three points lie on a straight line and a central point (B here) is between two others (A and C), it forms a flat angle.
Step 3: Recall that a flat angle is defined as an angle that measures 180∘, which is the total rotation a line undergoes around a single point.
Visual inspection of the diagram confirms that points A, B, and C create a straight line. Hence, the angle ∠ABC must be a flat angle.
Therefore, the angle ∠ABC is a flat angle.
Answer
Flat angle
Exercise #3
∢ABC is an angle measuring less than 90°.
What kind of angle angle is it?
Step-by-Step Solution
To determine what kind of angle ∠ABC is, let's examine the given information: the angle is less than 90∘.
Step 1: Recall the types of angles based on their measurements:
An acute angle measures less than 90∘.
A right angle measures exactly 90∘.
An obtuse angle measures greater than 90∘ but less than 180∘.
A flat angle measures exactly 180∘.
Step 2: Match the given information with these definitions.
Since ∠ABC measures less than 90∘, it fits the definition of an acute angle.
Therefore, the angle ∠ABC is an acute angle.
Answer
Acute angle
Exercise #4
Which figure depicts a right angle?
Video Solution
Step-by-Step Solution
A right angle is equal to 90 degrees.
In diagrams (a) and (c), we can observe that the angle symbol is a symbol representing an angle that equals 90 degrees.
Answer
Exercise #5
Which of the following angles are obtuse?
Video Solution
Step-by-Step Solution
By definition, an obtuse angle is an angle that is greater than 90 degrees. We can observe that in one drawing there is an angle of 90 degrees and therefore it is not an obtuse angle, the other two angles are less than 90 degrees meaning they are also not obtuse, they are acute angles.