HELP ME PLZ and show ur work if u can

An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression. To the nearest foot, how far is the boa

Yuri [45]

Answer:

407.22 foot is the boat from the base of the lighthouse

Step-by-step explanation:

Given the statement: An observer on top of a 50-foot tall lighthouse sees a boat at a 7° angle of depression.

Let x foot be the distance of the object(boat) from the base of the lighthouse

Angle of depression = $7^{\circ}$

$\angle CAB = \angle DCA = 7^{\circ}$ [Alternate angle]

In triangle CAB:

To find AB = x foot.

Using tangent ratio:

$\tan (\theta) = \frac{Opposite side}{Adjacent Base}$

$\tan (\angle CAB) = \frac{BC}{AB}$

Here, BC = 50 foot and $\angle CAB =7^{\circ}$

then;

$\tan (7^{\circ}) = \frac{50}{x}$

or

$x = \frac{50}{\tan 7^{\circ}}$

$x = \frac{50}{0.1227845609}$

Simplify:

AB = x = 407.217321 foot

Therefore, the boat from the base of the light house is, 407.22'

5 0

3 years ago

Q2) The following travel times were measured for vehicles traversing a 2,000 ft. segment of an arterial: Vehicle Travel Time (s)

adelina 88 [10]

Answer:

TMS = 45.78 m/s

SMS = 45.66 m/s

Step-by-step explanation:

Vehicle Travel Time (s)

1 40.5

2 44.2

3 41.7

4 47.3

5 46.5

6 41.9

7 43.0

8 47.0

9 42.6

10 43.3

Time mean speed and space mean speed are parameters used to express the speed of a group of vehicles in traffic flow.

Time mean speed is given as the average speed of all the cars

The speed for each vehicle is calculated by dividing the (2000 ft) distance by the time taken by each vehicle to complete that segment of the journey.

Let vehicle = V

Travel time = time

Speed = s

V | Time | speed (ft/s)

1 | 40.5 | 49.383

2 | 44.2 | 45.249

3 | 41.7 | 47.962

4 | 47.3 | 42.283

5 | 46.5 | 43.011

6 | 41.9 | 47.733

7 | 43.0 | 46.512

8 | 47.0 | 42.553

9 | 42.6 | 46.948

10| 43.3 | 46.189

TMS = (Σsᵢ)/N

Σsᵢ = (49.383+45.249+47.962+42.283+43.011+47.733+46.512+42.553+46.948+46.189)

Σsᵢ = 457.823

N = number of vehicles = 10

TMS = 457.823 ÷ 10 = 45.7823 = 45.782 m/s

b) Space mean speed is given as

SMS = N ÷ [Σ (1/sᵢ)]

V | Time | speed | (1/sᵢ)

1 | 40.5 | 49.383 | 0.02025

2 | 44.2 | 45.249 | 0.02210

3 | 41.7 | 47.962 | 0.02085

4 | 47.3 | 42.283 | 0.02365

5 | 46.5 | 43.011 | 0.02325

6 | 41.9 | 47.733 | 0.02095

7 | 43.0 | 46.512 | 0.02150

8 | 47.0 | 42.553 | 0.02350

9 | 42.6 | 46.948 | 0.02130

10| 43.3 | 46.189 | 0.02165

Σ (1/sᵢ) = (0.02025+0.02210+0.02085+0.02365+0.02325+0.02095+0.02150+0.02350+0.02130+0.02165)

Σ (1/sᵢ) = 0.219

SMS = 10 ÷ [Σ (1/sᵢ)] = 10 ÷ 0.219

SMS = 45.662 m/s

Hope this Helps!!!

4 0

3 years ago

What number represents the smallest value? .3 or .33

den301095 [7]

Answer:

.3

Step-by-step explanation:

.33 is .03 greater than .3

4 0

2 years ago

Zoe has 5 cucumbers she grew in her garden. she wants to share them equally amoug 4 of her neighbors. how many cucumbers will ea

Kazeer [188]

Each neighbor would get 1 whole cucumber and a 1/4 of a cucumber so it would be 1 and a 1/4

6 0

3 years ago

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The slant height of the top is 5 pm and the height of the cylinder is 9m find the distance between P and Q

Mashcka [7]

Answer:The slant height of the top is 5 m, and the height of the cylinder is 9 m. Find the distance between P and Q, to the nearest cm. 0 height of small triangle.

8 0

2 years ago