A triangle has sides 8 cm and 5 cm and an angle of 90 degrees between them.Calculate the smallest angle of the triangle
if the angle is x, then it is opposite the shortest side.
tan(x) = 5/8
5/8
To calculate the smallest angle of a triangle, you can use the trigonometric functions, specifically the sine function.
In this case, we have a right triangle with sides measuring 8 cm and 5 cm, and the right angle is given as 90 degrees. The other two angles are acute angles because the sum of all the angles of a triangle is always 180 degrees.
To find the smallest angle, let's calculate the sine of one of the acute angles. Since we have the lengths of the two sides and we need to find an angle, we can use the sine function with the side opposite the angle and the hypotenuse.
sin(A) = opposite/hypotenuse
In this case, the opposite side is the side measuring 5 cm, and the hypotenuse is the side measuring 8 cm.
sin(A) = 5/8
Now, we need to find the value of A. Taking the inverse sine (arcsine) of both sides, we have:
A = arcsin(5/8)
Using a calculator, we can find the value of arcsin(5/8) to be approximately 38.68 degrees.
Since this is one of the acute angles, the smallest angle of the triangle is 38.68 degrees.