question_answer 1)

                In a right triangle \[ABC,\,\angle B={{90}^{\text{o}}}\]. (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB.

Answer:

                (a) In the right triangle ABC, \[\because \]     \[\angle B={{90}^{\text{o}}}\]                    |Given \[\therefore \]  By Pythagoras theorem \[A{{C}^{2}}=A{{B}^{2}}=B{{C}^{2}}\] \[\Rightarrow \]               \[A{{C}^{2}}={{6}^{2}}+{{8}^{2}}\] \[\Rightarrow \]               \[A{{C}^{2}}=36+64\] \[\Rightarrow \]               \[A{{C}^{2}}=100\] \[\Rightarrow \]               \[AC=\sqrt{100}\]

	100
1	?1
20	00            ? 0
	0

  Therefore,                                                                                          . Hence, AC is equal to 10 cm. (b) In the right triangle ABC, \[\because \,\,\,\,\,\angle B={{90}^{\text{o}}}\]               |Given \[\therefore \]  By Pythagoras theorem \[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] \[\Rightarrow \]               \[{{13}^{2}}=A{{B}^{2}}+{{5}^{2}}\] \[\Rightarrow \]               \[169=A{{B}^{2}}+25\] \[\Rightarrow \]               \[A{{B}^{2}}=169-25\] \[\Rightarrow \]               \[A{{B}^{2}}=144\] \[\Rightarrow \]               \[AB=\sqrt{144}\]

	12
1	\[\overline{1}\]          \[\overline{44}\] ?1
22	44             ?44
	0

Therefore, \[\sqrt{144}\,=12\]. Hence, AB is equal to 12 cm.