Angles of Elevation & Depression Flashcards

All 5 cards in this deck

What is an angle of elevation?

The angle measured upwards from the horizontal to the line of sight of an object above.

What is an angle of depression?

The angle measured downwards from the horizontal to the line of sight of an object below.

True or false? The angle of depression from the top of a cliff to a boat equals the angle of elevation from the boat to the top of the cliff.

True.
The two horizontals are parallel, so the angles are alternate angles.

What are the steps to find a height from an angle of elevation?

e.g. standing 20 m from the foot of a tower, the angle of elevation of the top is $35^\circ$

1. Sketch the right-angled triangle: horizontal 20 m, angle $35^\circ$ at the observer, height $h$ opposite
2. Choose the ratio: $\tan 35^\circ = \dfrac{h}{20}$
3. Solve: $h = 20\tan 35^\circ = 14.0$ m (3 s.f.)

What are the steps to find an angle of elevation?

e.g. a tower 15 m high seen from a point 20 m from its foot

1. Sketch the triangle: opposite $= 15$, adjacent $= 20$, so use tan
2. Write: $\tan\theta = \dfrac{15}{20}$
3. Inverse: $\theta = \tan^{-1}(0.75) = 36.9^\circ$ (1 d.p.)