QuestionFind the angles of a triangle with a ratio of $5: 3: 4$ and identify the type of triangle based on these angles.

Studdy Solution

STEP 1

Assumptions1. The ratio of the sizes of the3 interior angles in a triangle is $534$ . . The sum of the interior angles in a triangle is $180^\circ$ .

STEP 2

First, we need to find the total parts in the given ratio. We can do this by adding all the parts of the ratio.
$Total\, parts =5 + +4$

STEP 3

Calculate the total parts in the ratio.
$Total\, parts =5 +3 + =12$

STEP 4

Now, we can find the size of each part in the ratio by dividing the total degrees in a triangle by the total parts.
$Size\, of\, each\, part = Total\, degrees / Total\, parts$

STEP 5

Plug in the values for the total degrees and the total parts to calculate the size of each part.
$Size\, of\, each\, part =180^\circ /12$

STEP 6

Calculate the size of each part.
$Size\, of\, each\, part =180^\circ /12 =15^\circ$

STEP 7

Now that we have the size of each part, we can find the sizes of the3 interior angles by multiplying the size of each part by the corresponding parts in the ratio.
$Angle\,1 =5 \\times Size\, of\, each\, part$ $Angle\,2 =3 \\times Size\, of\, each\, part$ $Angle\,3 =4 \\times Size\, of\, each\, part$

STEP 8

Plug in the size of each part to calculate the sizes of the3 interior angles.
$Angle\,1 =5 \\times15^\circ$ $Angle\,2 =3 \\times15^\circ$ $Angle\,3 =4 \\times15^\circ$

STEP 9

Calculate the sizes of the3 interior angles.
$Angle\, =5 \\times15^\circ =75^\circ$ $Angle\,2 =3 \\times15^\circ =45^\circ$ $Angle\,3 =4 \\times15^\circ =60^\circ$

STEP 10

Now that we have the sizes of the3 interior angles, we can name the type of the triangle. Since all the angles are less than $90^\circ$ , the triangle is an acute triangle.
The sizes of the3 interior angles in the triangle are $75^\circ$ , $45^\circ$ , and $60^\circ$ , and the triangle is an acute triangle.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms