Answer:
1) 8 cm
2) 15 ft
3) 3√10 ft = 9.5 ft (nearest tenth)
Step-by-step explanation:
Pythagoras’ Theorem
[tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Question 1
Given:
Substitute the given values into the equation and solve for x:
[tex]\implies 6^2+x^2=10^2[/tex]
[tex]\implies 36+x^2=100[/tex]
[tex]\implies x^2=100-36[/tex]
[tex]\implies x^2=64[/tex]
[tex]\implies x=\sqrt{64}[/tex]
[tex]\implies x=8\: \sf cm[/tex]
Question 2
Given:
Substitute the given values into the equation and solve for c:
[tex]\implies 9^2+12^2=c^2[/tex]
[tex]\implies 81+144=c^2[/tex]
[tex]\implies c^2=225[/tex]
[tex]\implies c=\sqrt{225}[/tex]
[tex]\implies c=15\: \sf ft[/tex]
Question 3
Given:
Substitute the given values into the equation and solve for c:
[tex]\implies 3^2+9^2=c^2[/tex]
[tex]\implies 9+81=c^2[/tex]
[tex]\implies c^2=90[/tex]
[tex]\implies c=\sqrt{90}[/tex]
[tex]\implies c=\sqrt{9 \cdot 10}[/tex]
[tex]\implies c=\sqrt{9}\sqrt{10}[/tex]
[tex]\implies c=3\sqrt{10}\: \sf ft[/tex]
