40- In a right triangle ABC, angle B = 90°.<br />a. If AB= 6 cm, BC = 8 cm, find AC<br />b. If AC=13 cm, BC= 5 cm, find AB About the author Remi
Answer: (a) Using Pythagoras theorem, AC^2=AB^2+BC^2AC 2 =AB 2 +BC 2 \Rightarrow AC^2=\left(6\right)^2+\left(8\right)^2⇒AC 2 =(6) 2 +(8) 2 \Rightarrow AC^2=\left(6\right)^2+\left(8\right)^2⇒AC 2 =(6) 2 +(8) 2 \Rightarrow AC^2=36+84=100⇒AC 2 =36+84=100 > AC = 10 cm (b) Using Pythagoras theorem, AC^2=AB^2+BC^2AC 2 =AB 2 +BC 2 \Rightarrow\left(13\right)^2=AB^2+\left(5\right)^2⇒(13) 2 =AB 2 +(5) 2 \Rightarrow169=AB^2+25⇒169=AB 2 +25 \Rightarrow AB^2=169-25⇒AB 2 =169−25 \Rightarrow AB^2=144⇒AB 2 =144 > AB = 12 cm Reply
Answer:
(a) Using Pythagoras theorem,
AC^2=AB^2+BC^2AC
2
=AB
2
+BC
2
\Rightarrow AC^2=\left(6\right)^2+\left(8\right)^2⇒AC
2
=(6)
2
+(8)
2
\Rightarrow AC^2=\left(6\right)^2+\left(8\right)^2⇒AC
2
=(6)
2
+(8)
2
\Rightarrow AC^2=36+84=100⇒AC
2
=36+84=100
> AC = 10 cm
(b) Using Pythagoras theorem,
AC^2=AB^2+BC^2AC
2
=AB
2
+BC
2
\Rightarrow\left(13\right)^2=AB^2+\left(5\right)^2⇒(13)
2
=AB
2
+(5)
2
\Rightarrow169=AB^2+25⇒169=AB
2
+25
\Rightarrow AB^2=169-25⇒AB
2
=169−25
\Rightarrow AB^2=144⇒AB
2
=144
> AB = 12 cm
Answer:
simple AC=13 and AB=6cm