Answer:
Options 1, 3 and 4 are true
Step-by-step explanation:
The legs EF and DF of the right triangle DEF have lengths of 24 units and 7 units, respectively. By the Pythagorean theorem,
[tex]DE^2=EF^2+DF^2\\ \\DE^2=24^2+7^2\\ \\DE^2=576+49\\ \\DE^2=625\\ \\DE=25\ units[/tex]
Find trigonometric functions:
[tex]\sin \angle D=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{EF}{DE}=\dfrac{24}{25}[/tex]
[tex]\cos \angle E=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{EF}{DE}=\dfrac{24}{25}[/tex]
[tex]\tan \angle D=\dfrac{\text{Opposite leg}}{\text{Adjacent leg}}=\dfrac{EF}{DF}=\dfrac{24}{7}[/tex]
[tex]\sin \angle E=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{DF}{DE}=\dfrac{7}{25}[/tex]
Thus, options 1, 3 and 4 are true
