Question

from point A on the ground the angle of elevation from the top of a flagpole is 53 deg. from point B on the other side of the pole the angle of elevation is 37 deg.
if AB=50 m and sin37= 0.6, find the height of the flagpole

Answer 1

Answer:

Let the height of the pole AB = x m. ∴ Length of shadow OB ol the pole AB = x m. Let the angle of elevation be ө, i.e. Hence, the angle of elevation of the Sun's altitude is 45°.

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Step-by-step explanation:

Examples: 1) From a boat on the lake, the angle of elevation to the top of the cliff is 24°22'. If the base of the cliff is 747 feet from the boat, how high is the cliff (to the nearest foot)? 2) From a boat on the river below a dam, the angle of elevation to the top of the dam is 24°8'.

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Answer 2

The height of the flagpole is 24 meters.

Given - Angle of elevation on both sides and distance AB

Find - Height of flagpole

Solution - Let the point of flagpole at group be O. So, assuming the distance between OB to be x. Thus, the distance between AO = (50-x).

We are aware that tan theta = perpendicular ÷base

Let the perpendicular or height of flagpole be x.

Now, for the position A

tan 53° = h÷(50-x)

For the position B

tan 37° = h÷x

Solving the equation of postion B to find the value of h.

0.75 = h÷x

h = 0.75x

Now, keep the value of h in equation of position A

1.33 = 0.75x÷(50 - x)

Shifting (50-x) to other side of equation and performing cross multiplication

66.5 - 1.33x = 0.75x

Shifting 1.33x to other side of equation and performing addition

2.08x = 66.5

Shifting 2.08x to other side of equation and performing division

x = 31.9

Rounding off the number to find the value of x

x = 32 m

Keep the value of x in equation of postion B

h = 0.75×x

h = 0.75×32

Performing multiplication

h = 24 m

Hence, the height of flagpole is 24 m.

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