find the missing length in the right triangle is sides are 14mi and 16mi?

Question

answers can be 15 mi, 60 mi, 7.7 mi or 30 mi

Answer 1

2 inches

Answer 2

Use a² + b² = c² to help you here.

Since we don't know which is the hypoteneuse -- the 14, the 16, or one of our answer choices -- let's just take the square of all of them and see if we can come up with three such that a² + b² = c²:

14 ² = 196
16 ² = 256
15 ² = 225
60 ² = 3600
7.7 ² = 59.29
30 ² = 900

It looks like 7.7 mi. is your answer (though the 7.7 is rounded). Notice that 196 + 60 = 256, so your two legs are the 14 mi. side and the 7.7 (rounded) mi. side, and the hypoteneuse is 16 mi.

ANSWER: 7.7 mi.

Hope that helped!

~ ♥ ~

Answer 3

Either 16 is the hypotenuse or the third , even longer side is

Either 14 squared + x squared = 16 squared

196 + x squared = 256....subtracting 196 from both sides,

x squared = 60,

making x a little bit less than 8.....(8sqd = 64)


Or 14 sqd + 16sqd = h sqd

196 + 256 = h sqd

452 = h sqd

h is a bit bigger than 20 and well under 25....(20sqd = 400, 25 sqd = 625)

h is just over 21


7.7 miles is a good solution.

There is another good solution, which is about 21 miles.

It depends on whether the missing side is the hypotenuse or whether it is one of the short sides.

Answer 4

Assume that the sides are not the hypotenuse, but it is the hypotenuse that we want to find:
missing length =sqr(14^2 + 16^2) = sqr(196+256) = sqr(452)
= 21.26 which does not match up with the choices yu have given. So let the hypotenuse be 16 and one of the sides be 14:
length^2 + 14^2 = 16^2
length^2 = 16^2 - 14^2 = 256 - 196 = 60 = 4x15
length = sqr(4x15) = 2sqr(15) = 2x3.8729833 = 7.7459...

Answer 5

This is an easy 3, 4, 5 triangle
therefore it is 15 mi

Answer 6

Use Pythagorean's Theorem. a^2 + b^2 = c^2
If those are the two short sides and one of them is not the hypotenuse then, plug in the sides that you do know into the "a" and "b" and solve for "c".
(14)^2 + (16)^2 = c^2
196 + 256 = c^2
Take the square root of both sides and whatever "c" equals is the answer.
452 = c^2
sqrt(452) = c
c = 21.3 mi
Which is not one of your answers so one of the sides must be the hypotenuse, so plug one of them into "c" and find "a" or "b". Since the hypotenuse is always longer than either side but shorter than both added together you know that 16 must be the hypotenuse in this case since it is not one of the sides (we already proved that).
a^2 + b^2 = c^2
(14)^2 + (b)^2 = (16)^2
196 + b^2 = 256
Solve for "b".
256 - 196 = b^2
60 = b^2
Take the square root of both sides.
sqrt(60) = b
b = 7.7mi
And that is one of the answers.

Answer 7

7.7 would be the answer

16 mi is the hypotenuse, and 14 mi is one of the sides

16^2=14^2+x^2
60=x^2
x=7.7

Answer 8

let say the hypo is unknown and let it be x
then x^2 = 14^2 + 16^2
x = 21.2, which is not there

so 16 is the hypo
then 16^2 = 14^2 + x^2
so x = 7.7

Answer 9

is 16 the hypotenues? or a leg?