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Dima020 [189]
3 years ago
9

the length of the shadow of a pole on level ground increases by 90m when the angle of elevation of the sun changes from 58 degre

e to 36 degree calculate correct to three significant figure the height of the pole

Mathematics
2 answers:
dezoksy [38]3 years ago
6 0

Answer:

height of pole = 121 m (to 3 significant figures

Step-by-step explanation:

From the diagram attached to this solution:

Let the length of the shadow = b

Let the height of the triangle = h

Triangle\ 1\\\\Tan\ (58)\ =\ \frac{h}{b}\\1.60\ =\ \frac{h}{b}  - - - - - -(1)\\\\

Tan\ (36) = \frac{h}{b+90} \\0.73\ =\ \frac{h}{b+90} - - - - (2)

From\ equation\ (1)\\1.60 = \frac{h}{b}\\ cross-multiplying\\1.60b = h - - - - - (3)\\\\\\from\ equation\ (2)\\0.73\ =\ \frac{h}{b+90}\\ corss-multiplying\\0.73b\ +\ 65.7 = h\\h\ =\ 0.73b\ +\ 65.7- - - - - -(4)\\

Notice that equation (3) = equation (4) = h

1.60b = 0.73b\ + 65.7\\1.60b\ -\ 0.73b\ = 65.7\\0.87b\ =\ 65.7\\b\ =\ \frac{65.7}{0.87} = 75.52\ m\\

Now let us find the height of pole from equation (3)

1.60b = h - - - - - - (3)

where b = 75.52

h = 1.60 × 75.52

h = 120.83 m

= 121 m (to three significant figure

Anarel [89]3 years ago
3 0

Answer:

The height of the pole is 167 m

Step-by-step explanation:

The given parameters are;

Increase  in the length of the shadow = 90 m

Initial angle of elevation of the Sun = 58°

Final angle of elevation of the Sun = 36°

We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase  in the length of the shadow  

We have by sin rule;

90/(sin (22°)  = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)

Let the initial ray from the top of the pole to the end of the shadow's length = l₁

90/(sin (22°)  = l₁/(sin(122°)

l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m

Therefore;

The height of the pole = 283.3 m × sin(36°) = 166.52 m

The height of the pole= 167 m to three significant figures.

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