a = 21
b = 21
Solution:
Figure (1): The given triangle is a right angle triangle.
One leg of the triangle (b) = 20
Hypotenuse of the triangle (c) = 29
Another leg of the triangle = a
Using Pythagoras theorem, find a:
[tex]Hypotenuse $^{2}=$ Base $^{2}+$ Height $^{2}$[/tex]
[tex]\Rightarrow 29^{2}=a^{2}+20^{2}[/tex]
[tex]\Rightarrow 841=a^{2}+400[/tex]
[tex]\Rightarrow 841-400=a^{2}[/tex]
[tex]\Rightarrow 441=a^{2}[/tex]
Taking square root on both sides, we get
⇒ a = 21
Hence a = 21 is the correct answer.
Figure (2): The given triangle is a right angle triangle.
One leg of the triangle (a) = 72
Hypotenuse of the triangle (c) = 75
Another leg of the triangle = b
Using Pythagoras theorem, find b:
[tex]Hypotenuse $^{2}=$ Base $^{2}+$ Height $^{2}$[/tex]
[tex]\Rightarrow 75^{2}=b^{2}+72^{2}[/tex]
[tex]\Rightarrow 5625=b^{2}+5184[/tex]
[tex]\Rightarrow 5625-5184= b^{2}[/tex]
[tex]\Rightarrow 441=b^{2}[/tex]
Taking square root on both sides, we get
⇒ b = 21
Hence b = 21 is the correct answer.
