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If the base angles of triangle are ((22 ...

If the base angles of triangle are `((22 1/2))^@` and `(112 1/2)^@` , then prove that the altitude of the triangle is equal to `1/2` of its base.

Text Solution

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In `Delta ABC, (BC)/(sin 45^(@)) = (AC)/(sin 22 (1)/(2)@)`
In `Delta ALC, (AL)/(AC) = sin 67 (1)/(2)@`

`AL = AC cos 22 (1)/(2)@`
`= (BC) /(sin 45^(@)) sin 22 (1)/(2)@ cos 22 (1)/(2)@` [using Eq. (i)]
`= (1)/(2) BC (sin 45^(@))/(sin 45^(@))`
`= (1)/(2) BC = (1)/(2) xx` Base
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