1. 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

3. Name the following sides of this triangle.

4.  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.

5.  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.

7.  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.

14.  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˚