$CATEGORY: Maths - TicTacLearn/7. Coordinate geometry/9. Some applications of trignometry--Heights and Distances

//Multiple Choice

The angle of elevation of the top of a tower is 30°. If the height of the tower is 40 m, the distance of the observer from the base of the tower is\: {
= 40√3 m
~ 40/√3 
~ 50m
~ None of the above
}

A man observes the angle of elevation of a tree to be 45°. If the height of the tree is 15 m, how far is he from its base? {
= 15m
~ 5m
~ 33m
~ None of the above
}

The height of a pole is 10 m, and its shadow is 10 m long. What is the angle of elevation of the sun? {
~ 30°
= 45°
~ 60°
~ 90°
}

The length of the shadow of a tower increases as the angle of elevation of the sun\: {
~ Increases
= Decreases
~ Remains constant
~ None of these
}

The angle of elevation of a ladder leaning against a wall is 60°. If the length of the ladder is 20 m, the height of the wall is\: {
~ 10 m
= 10√3m
~ 20√3m
~ 20m
}

If the height of a lighthouse is 90 m, and the angle of depression to a ship is 45°, the distance of the ship from the lighthouse is\: {
= 90m
~ 90√(2)m
~ 45m
~ 90/√2 m
}

The trigonometric ratio used to find the height of a building when the angle of elevation and distance from the base are known is\: {
~ sin⁡
~ cos⁡
= tan⁡
~ None of these
}

If the angle of elevation is 60°, the value of tan60° is\: {
~ 1
= √3
~ 1/√3
~ 3
}

The angle of elevation of a tower is 45°, and its shadow is 10 m long. The height of the tower is\: {
= 10m
~ 10√(2)m
~ 5m
~ 10√3 m
}

//True or False

The angle of depression is measured from the vertical line. {F}

tan⁡θ \= Opposite/Adjacent {T}

The shadow of an object decreases as the angle of elevation increases. {T}

sin⁡²θ + cos⁡²θ \= 1 {T}

The horizontal distance is always less than the height. {F}

tan⁡45° \= 1 {T}

The angle of depression is always smaller than 90°. {T}

For a right triangle, tan⁡60° \= √3. {T}

The distance to the object can be found without knowing the angle of elevation. {F}

The longer the shadow, the smaller the angle of elevation. {T}

//Numericals



//Fill in the blanks

The angle of elevation is measured _____ from the horizontal line. {
~ Downward
= Upward
~ Horizontally
}

The value of tan⁡30° is _____. {
= 1/√3
~ 1
~ √3
}

The shadow of a pole is longest when the angle of elevation is _____. {
~ 30°
~ 60°
= Smallest
}

The distance between the observer and the object is called the _____. {
~ Perpendicular
= Base
~ Hypotenuse
}

The trigonometric ratio used to find the distance of an object using the angle of depression is _____. {
= Tangent
~ Sine
~ Cosine
}

If the height of an object is 20 m and the angle of elevation is 45°, the horizontal distance from the observer is _____. {
= 20 m
~ 40 m
~ 10 m
}

tan⁡45°  is equal to _____. {
= 1
~ 1/2
~ 1/3
}

A tree 10 m tall casts a shadow 10 m long. The angle of elevation is _____. {
= 45°
~ 30°
~ 60°
}

//Match the following

Match the following items from Column A with their correct corresponding options from Column B\:
{
    =Horizontal distance -> Base
    =Shadow of an object -> Longer at sunrise
    =Height of an object -> Perpendicular distance
    =Angle of depression -> Downward angle
    =Distance calculation using tangent -> tanθ 
}



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