Trigonometric Ratios 8.2

Important terms to know: H (Hypotenuse) O (Opposite) Angle of Perspective A (Adjacent) Angle of perspective: this is the angle that you are either given or the angle that you are trying to find. (this is never the right angle) Hypotenuse: The side across from the right angle. Opposite side: This is the side across from the angle of perspective. Adjacent Side: This is the side next to your angle of perspective. (Not the hypotenuse)

Trigonometry Ratios SOH CAH TOA Remember…… S 𝑂 𝐻 Sin = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 C 𝐴 𝐻 Cos = 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 T 𝑂 𝐴 Tan = 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡

How to find a missing value Step 1: Mark the “Angle of Perspective”. Step 2: Label the sides (HOA). Step 3: Select a trigonometry ratio (sin/ cos / tan). Step 4: Substitute the values into the equation. Step 5: Solve the equation (Be sure your calculator is in Degrees)

Caution! Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

Example 1: Find the length of BC. Substitute. Cross multiply. Divide both sides by tan15° Put in calculator and Round to 2 places.

Example 2 Find the length. Round to the nearest hundredth. DF Substitute. Cross multiply, then divide both sides by sin 51°. Put in calculator and round to 2 places.

Example 3 Find the length. Round to the nearest hundredth. ST Substitute. Cross multiply. Put in calculator. Round to 2 places.