Question

. Given that O is the centre of the following circle, find the values of the unknowns.​

Answer 1

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

$a^{2} + 5^{2} = 13^{2}$

$a^{2} + 25 = 169$

$a^{2} = 169 - 25$

$a^{2} = 144$

$\sqrt{a^{2}}=\sqrt{144}$

$a = 12$

Now to find the value of 'b', i will use law of cosine,

$c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }$

$12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38$

Therefore, the values of 'a' and 'b' is 12 and 67.38 respectively

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