Given:
Radius of circle is 13 cm
Height of triangle is 5 cm
To find:
Value of 'a' and 'b'
Steps:
To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,
A² + B² = C²
[tex]a^{2} + 5^{2} = 13^{2}[/tex]
[tex]a^{2} + 25 = 169[/tex]
[tex]a^{2} = 169 - 25[/tex]
[tex]a^{2} = 144[/tex]
[tex]\sqrt{a^{2}}=\sqrt{144}[/tex]
[tex]a = 12[/tex]
Now to find the value of 'b', i will use law of cosine,
[tex]c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }[/tex]
[tex]12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38[/tex]
Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively
Happy to help :)
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