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From point A the angle of elevation to the top of a tall building is 20 degrees. on walking 80 m towards the building the angle of elevation is now 23 degrees. How tall is the building?

I just want to know how to draw the picture that's all.

Respuesta :

MissPhiladelphia
First, draw a diagram for a building. Then, from the top of the building, draw a slanting line down to the ground level. That angle is 20 degrees. Then draw another line from the top of the angle to the ground. But this time, nearer to the building. That angle would be 23 degrees. The distance at the ground level between the two lines is 80. The diagram would look like this:


Ver imagen MissPhiladelphia

The height of the building is 206.01 m.

The situation forms two right angle triangle with the same height. Therefore,

Right angle triangle

A right angle triangle has one of its side as 90 degrees.

The height of the building is the height(opposite side) of the triangle formed. The height can be found using trigonometric ratio.

Therefore,

tan ∅ = opposite / adjacent

Larger triangle

  • tan 20 =  opposite / 80 + x

Smaller triangle

  • tan 23 = opposite / x

Therefore,

(80 + x) tan 20 = opposite

x tan 23 = opposite

Hence,

(80 + x) tan 20 = x tan 23

80 tan 20 + x tan 20 = x tan 23

80 tan 20 = x tan 23 - x tan 20

80 × 0.36397023426 = x(0.42447481621 - 0.36397023426)

29.1176187413 = x(0.42 - 0.36)

0.06x = 29.12

x = 29.12 / 0.06

x = 485.333333333

x = 485.33

Therefore,

height of the building = 485.33 × tan 23

height of the building = 0.42447481621 × 485.33

height of the building = 206.010362551

height of the building = 206.01 m

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