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A person is standing at a distance of 80...

A person is standing at a distance of `80m` from the church looking at its top. The angle of elevation is `45^(@)`. The height of the church is.

Text Solution

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Let AB represent the church.
C is the position f the observer.
`angleACB` is the angle of elevation.
BC = 80 m, `angleACB = 45^@`. …(Given)
In right angled `triangleABC`.
`tan 45^@ = (AB)/(BC)` ...(By definition)
` therefore 1 = (AB)/(80)` ...(`tan 45^@ =1`)
`therefore` AB = 80 m
The height of the church is 80 m.
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Knowledge Check

  • A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is 30^(@) . What is the height of the lamp post?

    A
    50m
    B
    `50sqrt(3)m`
    C
    `(50)/(sqrt(3))m`
    D
    100m

  • A lamp post stands on a horizontal plane. From a point situated at a distance 150 m from its foot, the angle of elevation of the top is 30^(@). What is the height of the lamp post?

    A
    `50 m`
    B
    ` 50 sqrt3 m `
    C
    ` ( 50)/( sqrt3) m `
    D
    ` 100 m`