A right triangle has legs of 217 and 456. Find the perimeter exactly
Hint: the hypotenuse is a whole number
step 1
Find out the hypotenuse
Applying the Pythagorean Theorem
c^2=217^2+456^2
c^2=255,025
c=505
step 2
Find the perimeter
The perimeter of triangle is equal to
P=a+b+c
substitute the given values
P=217+456+505
P=1,178 units
therefore
the perimeter is 1,178 units
Part 2
see the attached image to better understand the problem
we have that
sin(theta)=456/505=0.90 --------> opposite side divided by the hypotenuse
cos(theta)=217/505=0.43-------> adjacent side divided by the hypotenuse
tan(theta)=456/217=2.10 -----> opposite side divided by the adjacent side