# Trigonometry.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.

justaguide | College Teacher | (Level 2) Distinguished Educator

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For a triangle ABC, the sides a, b and c and the angles A , B and C are related by :

sin A / a = sin B / b = sin C/ c

Here we know that one of the angles is 46 degrees and one is 90 degrees. So the third angle is 44 degrees.

sin 46/7 = sin 44/x

=>x = 7* sin 44/ sin 46

=> x = 6.759

The side opposite the third angle is 6.759 units

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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

TheĀ length of the missing side is x = 6.76 units.