Question

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

Answer 1

`(√(11) )/(5)`

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 =
`√(44)` (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 =
`√(44)` ÷ 10 =
`(√(11) )/(5)` (in surd form)