Trigonometric ratios can be used to solve real-life problems involving right triangles. To solve a triangle means finding the measures of all angles and sides. Common applications involve calculating angles of elevation or depression. When solving a right triangle, the problem should be drawn with proportional parts and labeled unknowns. Then, the appropriate trigonometric function can determine the missing pieces based on the information given.

1. Uses trigonometric ratios to
solve real life problems involving
right triangles

4. One of the main applications of trigonometry is solving triangles. To solve a triangle means to find the
measures of all the angles and sides of the triangle.
Two ideas that come up often in applications involve the angle of elevation and the angle of
depression. In solving a triangle, at least two parts are given. The other parts can be determined by using
the definition of trigonometric functions. When solving right triangle, it is good practice to draw the right
triangle whose parts are proportional to the given data.
Label these parts to easily identify the unknowns. Then use appropriate trigonometric functions to find
the unknown parts.

20. Six Trigonometric
Ratios
𝑠𝑖𝑛𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑐𝑠𝑐𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑐𝑜𝑠𝜃 =
𝑎𝑑𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑠𝑒𝑐𝜃 =
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑎𝑑𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑡𝑎𝑛𝜃 =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑐𝑜𝑡𝜃 =
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒