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

Answer:

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

Step-by-step 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

$A=37\°$

Answer 2

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