Question

If the sides of a triangle are 3, 4, and 5, then, to the nearest degree, the measure of the smallest angle of the triangle is...

Answer 1

arc tan(3/4) = 36.869 degrees round answer as necessary

Answer 2

The smallest angle of the triangle is
`37\°`

Explanation:

we know that

If the sides of a triangle are
`3`,
`4`, and
`5`, then

we have a right triangle

because, applying the Pythagoras theorem

`5^(2)=3^(2)+4^(2)`

`25=25` -------> is true

Remember that the measure of the smallest angle of triangle is the opposite angle to the smallest side

so

Let

A-------> the measure of the smallest angle

`tan(A)=3/4`

`A=arctan(3/4)=36.87\°`

Round to the nearest degree

`A=37\°`