Year 10

LLL - Trigonometry

Inverse Trig Angle Finder

Name the sides from the referred angle, choose the ratio, build the equation, then use inverse trig to find the angle.

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Find the angle from two sides.

This lesson slows inverse trig right down. Students name the sides first, choose sin, cos or tan, set up the equation, then use sin^-1, cos^-1 or tan^-1 to calculate the angle.

10side-name questions
20inverse trig calculations
1 dpangle answers
SOHsin uses opposite and hypotenuse
CAHcos uses adjacent and hypotenuse
TOAtan uses opposite and adjacent

The order

1mark the angle
2name the given sides
3choose the ratio
4build the equation
5use inverse trig

Side names

Opposite and adjacent depend on the angle

Hypotenuse is always across from the right angle. Opposite is across from the referred angle. Adjacent touches the angle but is not the hypotenuse.

Hypotenuse

long side

Always opposite the right angle.

Opposite and adjacent

look from theta

Opposite is across from theta. Adjacent is next to theta.

Inverse trig

Use inverse trig when the angle is missing

Once the side pair tells you the ratio, inverse trig turns the side fraction back into an angle.

Example

tan(theta) = opposite / adjacent

First write tan(theta) = opposite / adjacent.

Calculator

Use the inverse buttons on the calculator. Keep it in degrees.

Then use tan^-1(9 / 14) = 32.7 deg.
Section Question

Question

Question 1 of 30
0 / 10

Complete

Inverse trig summary

The key chain is: name sides, choose ratio, build the equation, use inverse trig, calculate the angle.

0 / 10side names
0 / 20angle calculations
0 / 30total