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Angles of Elevation & Depression
SOH CAH TOA
these angles are alternate, and equal
$$\sin\theta=\frac{opp}{hyp}$$ $$\cos\theta=\frac{adj}{hyp}$$ $$\tan\theta=\frac{opp}{adj}$$ A helicopter hovers 120m above one end of a landing strip. The pilot observes the angle of depression of the other end of the strip to be 22°. How long is the landing strip, to the nearest metre? 
remembering that the angle of elevation is alternate to the angle of depression $$\tan 22^{\circ}=\frac{120}{x}$$ 120 is opposite the angle and x is adjacent to it, so we will be using tan $$x=\frac{120}{\tan 22^{\circ}}$$ since x is the denominator, we will be diving, remember, the number always goes first x = 297.0104224 calculate x = 297m round to the nearest whole number 
From a point 40 metres from the base of a building, the angle of elevation to the top of the building is 48°. The angle of elevation to the top of the flagpole is 58°. Find the height of the flagpole.
Draw a triangle with the information provided
we will find x and y and then to get the height of the flagpole, subtract y from x$$\tan 58^{\circ}=\frac{x}{40}$$ since x is on the top, we multiply $$x=40\times{\tan 58^{\circ}}$$ remember, the number always goes first x = 64.01m calculate $$\tan 48^{\circ}=\frac{y}{40}$$ since y is on the top, we multiply $$x=40\times{\tan 48^{\circ}}$$ calculate y = 44.42m height of pole = 64.01 – 44.42
= 19.59mx – y
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