Question

Solve the right triangle below and round the decimal answers to the nearest tenth.

1. RS≈
2. RT≈
3. m∠T= (Note: This answer is a degree)


What are the answers for the following above?
Please show all the work on how you got your answers.

Answer 1

We know sum of interior angles in any triangle is 180°. Your specific triangle is a right triangle (one angle must be 90°) and we are also given another angle (57°) that means we can find angle T,

`T=180^(\circ)-90^(\circ)-57^(\circ)=33^(\circ)`

Use the sine function to find
`RT`,

`\sin(57^(\circ))=15/RT\implies RT=15/\sin(57^(\circ))\approx17.9`

Use the tangent function to find
`RS`,

`\tan(57^(\circ))=15/RS\implies RS=15/\tan(57^(\circ))\approx9.7`

Hope this helps.