Measurement – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Find shorter side lengths

Name the following sides of this triangle.

 Consider this right-angled triangle.  Labelling the sides with respect to the 42° angle, we can see that the unknown side is opposite and we are given the adjacent side.  Using our calculator, we know that the tangent ratio of a 42° angle is approximately 0.9.

 From the diagram,  We can now solve this equation to find the value of x. calculate adjacent opposite given size of an angle two sides  We are able to calculate an adjacent or opposite side length if we are given the size of an angle and one of these two sides.

 The steps used in solving the problem are as follows: 1. Label the sides of the triangle, which are either given, or need to be found, with respect to the given angle. 2. Use the tangent ratio to write a relationship between the opposite (O) and the adjacent (A) sides. 3. Substitute the values of the pronumerals into the ratio. 4. Solve the resultant equation for the unknown side length.

 It is possible to use the tangent ratio of either of the acute angles in the right-angled triangle. avoid pronumeral denominator  We can therefore avoid the situation where we are required to solve an equation with the pronumeral in the denominator.  Use the tangent of the other acute angle in the triangle to find the value of m. 68˚