# How do you calculate the length of the hypotenuse marked X in the triangle.We are given the magnitude of the angle as 23 degrees, opposite side is 30 and the hypotenuse is X.

justaguide | Certified Educator

Here we need to calculate the length of the hypotenuse. Now the angle given is 23 degrees, the opposite side is 30 and the hypotenuse is X.

We know that the sine value of an angle represents the opposite side divide by the hypotenuse.

Therefore sin 23 = 30 / X

Rearranging the terms we get : X = 30 / sin 23.

Now sin 23 = .3907

So X = 30/ .3907 = 76.77

So the length of the hypotenuse is 76.77

neela | Student

We can construct  a right angled triangle triangle ABC, with A = 23 degrees , B = 90 degrees, BC = 30  opposite to angle A.

Now AC = x.

Now opposite side to angle A / AC = sin A.

Or  BC/AC = sinA.

BC/sinA = AC hypotenuse = x.

Therefore x = BC/sin A = 30/sin23.

x = 30/ sin23 = 76.78 cm.

In a scientific calculator , ensure that you you are degree mode.Then  press button for sin, then press  button for number 2 then  button number 3 then equals . You now ger the value of sin23 which is 0.39073....

We convert angles in radians into degree. If an angle measures  a in radians, we covert into degree by mutiplying by 180/pi, where the value of pi is 3.14159...which is also available in a scientifica calculator.