Question

In right ΔDEF, DF = 20, m∠ F = 90˚, EF = 17. Which of the following is true? Does option 5 apply

Answer 1

Explanation:

From the picture attached,

ΔDEF is a right triangle with two sides,

EF = 17 units

DF = 20 units

By applying Pythagoras theorem in the given triangle,

DE² = DF² + EF²

(20)² = DF² + (17)²

DF² = 400 - 289

DF = √111

Trigonometric ratios for the ∠F,

sin(F) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

`\text{sin}F=(√(111))/(20)`

`\text{cosF}=\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`\text{cos}F=(17)/(20)`

`\text{tan}F=\frac{\text{Opposite side}}{\text{Adjacent side}}`

`\text{tan}F=(√(111))/(17)`

Choose the correct option.