Question

Use a trigonometric ratio to find the measure of 0 in the triangle below. Give your answer to the nearest degree. You may use the trigonometric functions of the Desmos scientific calculator:

Answer 1

• from trigonometric ratios:

`{ \boxed{ \rm{ \sin( \theta) = (opposite)/(hypotenuse) }}} \\`

• opposite → 9 cm

• hypotenuse → 10 cm

`{ \rm{ \sin( \theta) = (9)/(10) }} \\ \\ { \rm{ \theta = { \sin }^( - 1)( (9)/(10)) }} \\ \\ { \boxed{ \rm{ \theta = 64.2 \degree}}}`

Answer 2

`\\ \sf\longmapsto sin\Theta=(Perpendicular)/(Hypotenuse)`

`\\ \sf\longmapsto sin\Theta=(9)/(10)`

`\\ \sf\longmapsto sin\Theta=0.9`

`\\ \sf\longmapsto sin^(-1)\Theta=sin^(-1)(0.9)`

`\\ \sf\longmapsto \Theta=64.15°`