Answer:
[tex]1.\ x = 5\ in[/tex]
[tex]2.\ x = 5\ mi[/tex]
[tex]3.\ x = 8.6\ km[/tex]
[tex]4.\ x= 14.1\ mi[/tex]
Step-by-step explanation:
Given
See attachment for triangles
Required
Determine the missing sides
All 4 triangles are right-angled. So, to calculate the missing sides, we apply Pythagoras theorem which states that:
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
Solving (1):
[tex]Hypotenuse = 13[/tex]
So, we have:
[tex]13^2 = 12^2 + x^2[/tex]
[tex]169 = 144 + x^2[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2 = 169 - 144[/tex]
[tex]x^2 = 25[/tex]
Take positive square root of both sides
[tex]x = \sqrt{25[/tex]
[tex]x = 5\ in[/tex]
Solving (2):
[tex]Hypotenuse = x[/tex]
So, we have:
[tex]x^2 = 4^2 + 3^2[/tex]
[tex]x^2 = 16 + 9[/tex]
[tex]x^2 = 25[/tex]
Take positive square root of both sides
[tex]x = \sqrt{25[/tex]
[tex]x = 5\ mi[/tex]
Solving (3):
[tex]Hypotenuse = 14.7[/tex]
So, we have:
[tex]14.7^2 = x^2 + 11.9^2[/tex]
[tex]216.09 = x^2 + 141.61[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2 = 216.09 - 141.61[/tex]
[tex]x^2 = 74.48[/tex]
Take positive square root of both sides
[tex]x = \sqrt{74.48[/tex]
[tex]x = 8.6\ km[/tex]
Solving (4):
[tex]Hypotenuse = 15.4[/tex]
So, we have:
[tex]15.4^2 = x^2 + 6.3^2[/tex]
[tex]237.16 = x^2 + 39.69[/tex]
Make [tex]x^2[/tex] the subject
[tex]x^2= 237.16 - 39.69[/tex]
[tex]x^2= 197.47[/tex]
Take positive square root of both sides
[tex]x= \sqrt{197.47[/tex]
[tex]x= 14.1\ mi[/tex]
