One leg of a triangle is 10 inches, and the hypotenuse is 12 what is the tangent of the triangles second smallest interior angle ?

Step-by-step explanation:

One leg of a triangle is 10  inches.

Hypotenuse is 12 inches.

To find the other leg, we apply the Pythagorean formula:

a² + b² = c² (Where a and b are the legs of a triangle and c is the hypotenuse)

So if we need to find the length of the other leg of our triangle, we do this;

a² = c² - b²

a² = 12² - 10² = 44

a = (the length of the shortest leg)

The shortest angle of this right-triangle is opposite to the shortest leg.

To find the tangent of this shortest angle, we divide;

Tan angle = opposite ÷ adjacent = ÷ 10 = (in surd form)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.