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Daniel [21]
2 years ago
14

A flagpole sits on the top of a cliff that is 25 m above sea level. If the angle of elevation from a boat on the water to the to

p of the cliff is 29 degrees and the angle of elevation from the boat to the top of the flagpole is 32 degrees, determine the height of the flagpole (rounded to one decimal place).
Mathematics
1 answer:
OLEGan [10]2 years ago
6 0

Answer:

3.2 m

Step-by-step explanation:

Let x be the distance between the cliff and the boat.

Since the cliff is 25 m above sea level and the distance between the boat and the height of the cliff are perpendicular, and the line of sight of the boat to the base of a cliff is 29 , these three form a right-angled triangle with hypotenuse side as the line of sight of the elevation of the boat to the base of the cliff.

So, using trigonometric ratios, tan29° = 25/x

x = 25 m/tan29° = 25 m/0.5543 = 45.1 m

Also, the line of sight of the top of the flagpole, the cliff and the distance between the boat and the cliff form a right-angled triangle with hypotenuse side as the line of sight of the top of the flagpole,

Now, the angle of elevation of the top of the flagpole from the top of the boat is 32°, we now find the angle opposite to x, the distance from the boat to the cliff.  

Since it is a right-angled triangle, thus one angle is 90° and the unknown angle is A.

So, 90° + 32° + A = 180° (sum of angles in a triangle)

122° + A = 180°

A = 180° - 122°

A = 58°

Let y be the length of the flagpole. In this same triangle, using the sine rule, with x being the side opposite A and 25 + y being the side opposite the 32° angle, where 25 + y = height of cliff + length of flagpole, then

x/sinA = (25 + y)/sin32°

25 + y = xsin32°/sinA

y =  xsin32°/sinA - 25

y = 45.1sin32°/sin58° - 25

y = 45.1 × 0.5299/0.8480 - 25

y = 45.1 × 0.6249 - 25

y =28.183 - 25

y = 3.183

y ≅ 3.2 m to one decimal place

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2 years ago
Luke can paint 91 portraits in 7 weeks.
dimulka [17.4K]
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What is the measure of angle 4?​
LUCKY_DIMON [66]

Answer: Where is angle 4?? Not enough info

8 0
2 years ago
(05.05 LC)
Phantasy [73]

Answer:

A. $6

Step-by-step explanation:

We are given the table representing the number of days and the total charges in dollars.

So, the rate of change of the amount is given by, \frac{16-6}{1-0}=\frac{26-16}{2-1}=10

The linear equation representing the situation is,

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So, substituting the rate and the point (0,6), we get,

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4 0
3 years ago
when 55 is added to a certain number and the sum is divided by 3 , the result is 4 times the original number what is the origina
gogolik [260]

Answer:

4.99

Step-by-step explanation:

i cant remember how i got 4.99 but can show u how to check

= 55 +<u> 4.99 </u>= 59.99

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2 years ago
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