Obtuse Triangle

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

Homework:

Calculate which is larger

Given that the triangle $\triangle ABC$ is an obtuse triangle.

Which angle is larger $∢B$ or $∢A$?

Solution:

Since we are given that the triangle $\triangle ABC$ is an obtuse triangle, we understand that $∢B$ is not greater than $90°$.

In a triangle, there is only one obtuse angle therefore the answer is: $∢B>∢A$

Answer: $∢B>∢A$

Given the triangle $\triangle ABC$.

$∢B$ is obtuse.

The sum of the acute angles in the triangle is equal to $70°$.

Find the value of angle $∢B$.

Solution:

Since we know that $∢B$ is obtuse, we are certain that angles $∢A$ and $∢C$ are acute.

This means that we have the information that the sum of the acute angles $∢B+∢A=70°$

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

$70°+∢B=180°$

$∢B=110°$

Answer:

$∢B=110°$

Given the obtuse triangle $\triangle ABC$.

$∢C=\frac{1}{2}∢A$,$$

$∢B=3∢A$

Task:

Is it possible to calculate $∢A$?

If so, calculate it.

Solution:

Given that:

$∢C=\frac{1}{2}∢A$

$∢B=3+∢A$

We substitute:

$∢A=α$

$∢B=3α$

$∢C=\frac{1}{2}α$

$α+3α+\frac{1}{2}α=180°$

$4.5α=180°$

$α=40°$

Answer: yes, $40°$.

Assignment

Which triangle is given in the drawing?

Solution

Since angles $ABC$ and : $ACB$ are both equal to $70^o$, we know that the opposite sides are also equal, therefore the triangle is isosceles.

Answer

Isosceles triangle

Assignment

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

Solution

Let's observe triangle $A$ and check if it satisfies the Pythagorean theorem, therefore we replace the data we have:

$5^2+8^2=9^2$

We solve the equation

$25+64=81$

$89>81$

The sum of the squares of the "perpendicular" is greater than the square of the rest, therefore the triangle is an isosceles triangle.

Let's observe triangle $B$ and check if it satisfies the Pythagorean theorem, therefore we replace the data we have:

$7^2+7^2=13^2$

We solve the equation

$49+49=169$

$98<169$

The sum of the squares of the "perpendicular" is less than the square of the other, therefore the triangle is obtuse

Let's observe triangle $C$ and check if the Pythagorean theorem is satisfied, first we calculate what is the square root of $113$

$\sqrt{113}\approx10.6$

This is the largest side among the: $3$ and we will refer to it as "hypotenuse".

Now we replace the data we have:

$7^2+8^2=\sqrt{113}^2$

We solve the equation

$49+64=113$

$113=113$

In this triangle, the Pythagorean theorem is satisfied and therefore the triangle is right.

Answer

A: acute angle B: obtuse angle C: right angle