# A triangle has a right angle and the side opposite the angle 46 degrees is 7 units. Find the length of the side opposite the third angle.

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As the triangle has a right angle we can determine the third angle as 180- 90- 46 = 90 - 46 = 44.

Now the side opposite 46 degrees is 7.

=> sin 46 = (7/h), h denotes the hypotenuse.

=> h = 7/ sin 46

To find the otter side, we use the sine of the other angle.

Sin 44 = x/ h

=> sin 44 = x / (7/ sin 46)

=> x = sin 44* 7/ sin 46 = 6.759.

**Therefore the required side has a length 6.759 units.**

Let ABC be the right angled triangle with 90 degree at B and 46 degree at A.

The opposite side to angle46 degree is BC. BC = 7 by data.

Therefore BC/AB = tan A

=> tanA = tan 46 = BC/AB.

=> AB tan A = BC.

=> AB = BC/tan46 = 7/tan46 = 7/ 1.03553 = 6.76.

Therefore the other side that includes 90 degree is BC = 6.76 units.

We conclude that we are looking for the length of the side of a triangle.

We'll note the missing side as x. If the included angle is 90 degrees, we'll conclude that the triangle is right angled.

Knowing an angle and it's opposed side and looking for the other leg of the right triangle, we'll apply the tangent function.

tan 46 = 7/x

Tan 46 = 1.0355

1.0355 = 7/x

We'll multiply by x:

1.0355x = 7

We'll divide by 1.0355:

x = 7/1.0355

x = 6.76 units

**The length of the missing side is x = 6.76 units.**