# Solve Right Angled Triangle Problems We have two choices, we can solve Either gives the same answer, (x)]. For a given triangle in which only one side is known, two possible triangles can be formed.

We have two choices, we can solve Either gives the same answer, (x)]. For a given triangle in which only one side is known, two possible triangles can be formed.Take a look: The magenta sides mark out an obtuse triangle (small one on the left) and an acute triangle (outer triangle) using the same combination of two sides, where the third (bottom) side can be one of two lengths because it isn't initially known. First, we solve for angle A using the LOS: We can rearrange and use the inverse sine function to get the angle: Now if there is an ambiguity, its measure will be 180˚ minus the angle we determined: Now if that angle, added to the original angle (30˚) is less than 180˚, such a triangle exist, and we have an ambiguous case. If so, that might be enough to resolve the ambiguity.This section looks at Sin, Cos and Tan within the field of trigonometry.

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A right triangle consists of two legs and a hypotenuse.

The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.

Check for ambiguities unless you're clear about the results from other clues in the problem.

The law of cosines is computationally a little more complicated to use than the law of sines, but fortunately, it only needs to be used once.

Step-by-step explanations are provided for each calculation.

One of the best known mathematical formulas is Pythagorean Theorem, which provides us with the relationship between the sides in a right triangle.

The opposite side is opposite the angle in question.

In any right angled triangle, for any angle: The sine of the angle = the length of the adjacent side So in shorthand notation: sin = o/h cos = a/h tan = o/a Often remembered by: soh cah toa Example Find the length of side x in the diagram below: The angle is 60 degrees.

After the law of cosines is applied to a triangle, the resulting information will always make it possible to use the law of sines to calculate further properties of the triangle.

Consider another non-right triangle, labeled as shown with side lengths x and y.

## Comments Solve Right Angled Triangle Problems

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