Elevation & Depression

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#18710

Angles of Elevation & Depression

SOH CAH TOA

these angles are alternate, and equal

$$\sin\theta=\frac{opp}{hyp}$$

$$\cos\theta=\frac{adj}{hyp}$$

$$\tan\theta=\frac{opp}{adj}$$

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#18711

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

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#18713

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 = 19.59m	x – y

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