Question

Question #04dfb

Answer 1

`"It is an obtuse angled triangle"`

Explanation:

We need to know this to find the answer

First we need to assign the values (sides)

`color(blue)(a=34`

`color(blue)(b=20`

`color(blue)(c=47` `"(longest side)"`

Now, we can check the type of the triangle

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(orange)(rArra^2+b^2squarec^2`

`color(orange)(rArr34^2+20^2square47^2`

`color(orange)(rArr1156+400square2209`

`color(green)(rArr1150<2209`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can clearly say that it is an obtuse angled triangle as it follows the rule `color(blue)(a^2+b^2< c^2`

Answer 2

It is an obtuse triangle. See explanation.

Explanation:

A triangle is accute when all its angles are accute (i.e. less than `90^o`)

A triangle is right when it has a right angle (`90^o`)

A triangle is obtuse if it has an obtuse angle (i.e. more than `90^o`)

To check if a triangle is right, accute or obtuse you have to find out if the angle opposite to the longest side is right, obtuse or accute. This is the largest angle so only it can be right or obtuse. To do so you can use the Cosine Law.

The law tells that for every triangle it is true that:

`c^2=a^2+b^2-2abcosgamma`

From this formula you can tell that:

• If `c^2 < a^2+b^2` then `gamma<90` (i.e. triangle is accute)
• else if `c^2=a^2+b^2` then `gamma=90` (triangle is right)
• else if `c^2 > a^2+b^2` then `gamma>90` (triangle is obtuse)

Here we have: `c=47`, `a=20` and `b=34`

`c^2=2209` and `a^2+b^2=400+1156=1556`

We see that `c^2>a^2+b^2` so according to last point triangle is obtuse.