Trigonometric Ratios

Set up and Solve for missing sides and angles

SOH CAH TOA

Trig Ratios and Right Triangles

The sides of the triangle have names, but it depends on the angle you are looking from.From angle A – BlueFrom angle B – Red

Describing the Sides

• Opposite side in relationship to angle usingAcross from the angle, does not touch the

angle we are using• Adjacent angle in relationship to angle using

Touches the angle, not hypotenuse, connects angle to right angle

• HypotenuseAlways the longest side, across from the

right angle

Trig Ratios

The trigonometric value of an angle is related to a specific ratio of two of the sides of the triangle

adj

opgent

hyp

adjine

hyp

oppe

tantan

coscos

sinsinSOH

CAH

TOA

Set up

1. Determine Trig ratio you are using - You need to know what angle you are given or need to find, then know what sides you are using in relationship to that angle

2. Set up trig ratio3. Solve trig ratio

1. If unknown is in numerator then trig value of angle times denom

2. If unknown is in denominator then numerator divided by trig value of angle

3. If angle is unknown then inverse trig value of the ratio of sides

Examples

Examples Continued

Example Continued

• When an 18 ft ladder is leaning against a wall and it makes a 68 degree angle with the ground. How high up the wall does the ladder reach?