Question

PLEASE HELP ME ASAP PLEASE!!!

If c is the hypotenuse of a right triangle, find the missing side. If necessary, round to the nearest hundredth.
c= 155, b = 31, a =[ ]

Answer 1

a= 151.87 units

Explanation:

Given:

Consider,a right triangle Δ ACB with Angle C as 90°,

and side a, b, and c be the sides opposites to the respective angles. Such that

c = Hypotenuse = 155

b = Shorter leg = 31

a = Longer leg = ?

To Find:

a = Longer leg = ?

Solution:

In Right angle Δ ACB

If we apply Pythagoras Theorem we get

`(\textrm{Hypotenuse})^(2) = (\textrm{Shorter leg})^(2)+(\textrm{Longer leg})^(2)`

Now substituting the given above values we get,

`c^(2)= b^(2) + a^(2)\\x^(2)  155^(2)= 31^(2)+ a^(2)\\ 24025=961+a^(2)\\\therefore a^(2)=24025-961\\a^(2) = 23064\\ a=\pm 151.8683\\\therefore a = 151.87 .......\textrm{Distance cannot be in negative}`

∴ a= 151.87 units......(rounded to nearest hundredth)