Answer:
[tex]\frac{\sqrt{11} }{5}[/tex]
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 = [tex]\sqrt{44}[/tex] (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 = [tex]\sqrt{44}[/tex] ÷ 10 = [tex]\frac{\sqrt{11} }{5}[/tex] (in surd form)
