L4.9 - Using Trigonometric Ratios to Find Angles
Learning Intentions and Success Criteria
We are learning to:
- Calculate angle measures in right triangles using arccosine, arcsine, and arctangent
- Use arccosine, arcsine, and arctangent to find angle measures in right triangles
9.1: Once More with the Table
A triangle with side lengths 3, 4, and 5 is a right triangle by the converse of the Pythagorean Theorem. What are the measures of the acute angles?
![Image](https://stage.geogebra.org/resource/by9cvpfh/x8ZKNdieXVcHnFtu/material-by9cvpfh.png)
![Image](https://stage.geogebra.org/resource/tysvbsmw/EiJLwIMu8A5mi6a9/material-tysvbsmw.png)
tan() = To solve this for angle degree use tan(3/4) on the calculator is also called arctangent.
9.2: From Ratios to Angles
![9.2: From Ratios to Angles](https://stage.geogebra.org/resource/q4akzcxv/1hhnQFfDZb2SCBYT/material-q4akzcxv.png)
ABC
DEF
GHJ
![Image](https://stage.geogebra.org/resource/nxgre2se/JylBgUP5kzj9Lh6X/material-nxgre2se.png)
![Image](https://stage.geogebra.org/resource/druxzauz/1ve0oCmkVwmNfBvh/material-druxzauz.png)
Learning Intentions and Success Criteria
We are learning to:
- Calculate angle measures in right triangles using arccosine, arcsine, and arctangent
- Use arccosine, arcsine, and arctangent to find angle measures in right triangles
Cool-Down: Again with the Calculator
A triangle with side lengths 8, 15, and 17 is a right triangle by the converse of the Pythagorean Theorem. What are the measures of the other 2 angles?
![Image](https://stage.geogebra.org/resource/dugrd7gb/e9EdSTGj76k7b4Ol/material-dugrd7gb.png)
![Image](https://stage.geogebra.org/resource/ntefyrq4/d7Z2Pb5zvpEuwDt8/material-ntefyrq4.png)
![Image](https://stage.geogebra.org/resource/d5phwhmj/TdkenKRzldOe62aD/material-d5phwhmj.png)
![Image](https://stage.geogebra.org/resource/fqyxpuuw/HuXt5jsE17CXoALk/material-fqyxpuuw.png)