Indirect Measurement and Trigonometry Algebra 2 Mr. Seavy

Example 1 How would you find the value of x? You can use the Pythagorean Theorem because it is a right triangle with two sides given.

Example 2 How would you find the value of S? First you must know that the triangles are similar.

Similarity Two polygons are similar if….. their corresponding angles are congruent Congruent: equal measurement AND their corresponding sides are proportional Proportional: having equal ratios or scale Ex: 3 times bigger, shrunk by ¼, 5.23 times bigger Similar figures are commonly seen in shadow problems or when a dilation is performed.

Similarity Example Find a and b.

Example 3 How would you find the values of a and c in this triangle? We need a new method because we do not have two sides.

Trigonometry Ratios

Identify Trig Ratios

Example Draw the following situation: A 12 ft ladder is leaning up against a wall. The angle between the ladder and the ground is 58o. How high up the wall will the ladder go?

Applying Trig Ratios

Additional Practice Find x and y.

Finding an angle given the sides Use the inverse trig functions found in the calculator to figure out the measure of an angle given the measurements of the sides. sin-1, cos-1, tan-1

Examples Find the measure of the indicated angle using the ratio of your choice.