The angle of elevation is formed when an observer looks ___ at an object.

Upward

The angle of depression is formed when an observer looks ___ at an object.

Downward

In trigonometry, which ratio is used to calculate height given the angle of elevation and distance?

Tan θ = height/distance

If the height of a tower is represented as h and the angle of elevation is θ, the formula used is tan θ = h/___

Distance

True or False: The angle of elevation from point A to point B is equal to the angle of depression from point B to point A.

True

If a tower casts a shadow of length L, and the height is H, the angle of elevation θ can be found using tan θ = H/___

L

A guard observes an enemy boat at an angle of depression of 29°. If the tower height is 180 m, the horizontal distance to the boat is approximately ___ m.

325

Fill in the blank: The relation tan θ = ___/___ is crucial for finding heights in trigonometric calculations.

Height/distance

From a height of 25 m, if the angle of elevation to a cloud is 30°, the height of the cloud can be found using which trigonometric function?

Tan

If the angle of elevation of a tower is 30° and the distance from the observer is 120 m, the tower's height is approximately ___ m.

69.28

From the top of a 20 m pole, if the angle of elevation to a tower is 60°, the height of the tower can be expressed as ___ m.

80

True or False: The height of a tower can be calculated using only the angle of depression without knowing the distance.

False: The distance is also needed to calculate the height.

If the height of a tower is h and the distance to the observer is d, what is the mathematical expression for tan θ?

H/d

What trigonometric ratio would you use to calculate the distance from a point to the foot of a tower given its height and the angle of elevation?

Tan

If a tower's height is represented as h and the distance from the observer to the tower is d, express the angle of elevation θ in terms of h and d using the tangent function.

Tan θ = h/d