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)}=√(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=√(169 + 25-130(cos\beta ))\\12=√(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

Happy to help :)

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