Answer:
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
Step-by-step explanation:
Note that tan 60 degrees = (length of longer leg) / (length of shorter leg), or
tan 60 degrees = (length of longer leg) / 4 in.
Thus, (length of longer leg) = (4 in)(tan 60 degrees)
= (4 in) [√3/1] = 4√3 in
Also, cos 60 degrees = (adjacent side) / (hypotenuse. We want to find the hypotenuse and thus solve this equation for it:
(hypotenuse) = (adjacent side) / (cos 60) = (4 in)( 2/1 ) = 8 in
The length of the hypotenuse is 8 inches; the length of the longer leg is 4√3 inches.
