Answer:
a= 151.87 units
Step-by-step 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
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Now substituting the given above values we get,
[tex]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}[/tex]
∴ a= 151.87 units......(rounded to nearest hundredth)
