What is the angle of depression from the top, №12169961, 22.09.2021 05:08

Mathematics

The lighthouse keeper that is at the top of a lighthouse that is 88 ft tall. A ship is sighted that is 1532 ft from the base of the lighthouse. What is the angle of depression from the top of the lighthouse to the ship? Round to the nearest hundredth. OA) 18.02° OB) 9.6° OC) 3.29° OD 17.41°

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

Let θ be the angle of depression i.e the angle between the horizontal and the observer's line of sight.

tanθ= (Height of the light house)/(Horizontal distance of ship from the base of light house)

∴tanθ=88/1532=0.0574

∴θ=tan−1(0.0574)=3.290(2dp)

Mathematics

The lighthouse keeper that is at the top of a lighthouse that is 88 ft tall. A ship is sighted that is 1532 ft from the base of the lighthouse. What is the angle of depression from the top of the lighthouse to the ship? Round to the nearest hundredth. OA) 18.02° OB) 9.6° OC) 3.29° OD 17.41°

Step-by-step answer

P Answered by PhD

1

Step-by-step explanation:

Let θ be the angle of depression i.e the angle between the horizontal and the observer's line of sight.

tanθ= (Height of the light house)/(Horizontal distance of ship from the base of light house)

∴tanθ=88/1532=0.0574

∴θ=tan−1(0.0574)=3.290(2dp)

Mathematics

Alighthouse is 90 feet above sea level. the angle of depression from the top of the lighthouse to the center of the rock is 35 degrees, and the angle of depression to the swimmer is 45 degrees. find the distance between the center of the rock and the swimmer.

Step-by-step answer

P Answered by PhD

Notice the picture below

so.... the angle of depression, is above in dashed lines.... however, the angle of depression, is identical to the angle of elevation from the water, since, both angles are "alternate interior" angles

now, using the 45-45-90 rule, then we know the swimmer is 90 feet from the lighthouse, then just use the tangent ratio to get "x"
Alighthouse is 90 feet above sea level. the angle of depression from the top of the lighthouse to th

Alighthouse is 90 feet above sea level. the angle of depression from the top of the lighthouse to th

Mathematics

Jennifer stands 80 ft above sea level at the top of a lighthouse. she sees a boat sailing 400 ft from the lighthouse.what is the angle of depression from the top of the lighthouse to the boat? round to the nearest whole degree.

Step-by-step answer

P Answered by PhD

32

Let

X= the altitude of the lighthouse above sea level= 80 ft

A = the angle of depression

Y= the distance of the boat from the lighthouse= 400 ft

tan A=X/Y > 80/400=0.2

arctan (0.2)=11.31 degree

The answer is the angle of depression is 11 degree

Mathematics

Alighthouse is 90 feet above sea level. the angle of depression from the top of the lighthouse to the center of the rock is 35 degrees, and the angle of depression to the swimmer is 45 degrees. find the distance between the center of the rock and the swimmer.

Step-by-step answer

P Answered by PhD

Notice the picture below

so.... the angle of depression, is above in dashed lines.... however, the angle of depression, is identical to the angle of elevation from the water, since, both angles are "alternate interior" angles

now, using the 45-45-90 rule, then we know the swimmer is 90 feet from the lighthouse, then just use the tangent ratio to get "x"
Alighthouse is 90 feet above sea level. the angle of depression from the top of the lighthouse to th

Mathematics

In guiding a ship past dangerously shallow water, a light house attendant must determine the distance of the ship from the lighthouse. the lighthouse attendant sights the ship 30 degrees down from the horizontal. this 30 degrees angle is called the angle of depression. if the top of the lighthouse is about 200 feet above the sea level, how far is the ship from the base of the light house? express your answer to the nearest foot. a) 346 ft b) 115 ft c) 173 ft d) 100 ft

Step-by-step answer

P Answered by PhD

2

check the picture below.

make sure your calculator is in Degree mode.

Mathematics

In guiding a ship past dangerously shallow water, a light house attendant must determine the distance of the ship from the lighthouse. the lighthouse attendant sights the ship 30 degrees down from the horizontal. this 30 degrees angle is called the angle of depression. if the top of the lighthouse is about 200 feet above the sea level, how far is the ship from the base of the light house? express your answer to the nearest foot. a) 346 ft b) 115 ft c) 173 ft d) 100 ft

Step-by-step answer

P Answered by PhD

2

check the picture below.

make sure your calculator is in Degree mode.

Mathematics

The angle of depression from the top of a lighthouse to a boat is 27*. if the direct distance from the top of lighthouse to the boat is 462 ft, find the distance from the base of the lighthouse to the boat

Step-by-step answer

P Answered by Master

Correct Db = 411 .18 ft

Step-by-step explanation:

Given:

α = 27° angle of depression

Dt = 462 ft distance from the top of lighthouse to the boat

Db = ? distance from the base of the lighthouse to the boat

Here we have a right triangle with hypotenuse Dt and one leg Db.

By definition

cos α = Db / Dt ⇒ Db = Dt · cos α

Db = 462 · cos 27° = 462 · 0.89 = 411 .18 ft

Db = 411 .18 ft

God is with you!!!

Mathematics

Jennifer stands 80 ft above sea level at the top of a lighthouse. she sees a boat sailing 400 ft from the lighthouse.what is the angle of depression from the top of the lighthouse to the boat? round to the nearest whole degree.

Step-by-step answer

P Answered by PhD

32

Let

X= the altitude of the lighthouse above sea level= 80 ft

A = the angle of depression

Y= the distance of the boat from the lighthouse= 400 ft

tan A=X/Y > 80/400=0.2

arctan (0.2)=11.31 degree

The answer is the angle of depression is 11 degree

Mathematics

The angle of depression from the top of a lighthouse to a boat in the water is 30°. if the lighthouse is 89 feet tall how far is the boat from the lighthouse to the nearest foot? a) 45 feet b) 51 feet c) 63 feet d) 154 feet

Step-by-step answer

P Answered by PhD

12

D) 154 feet

Step-by-step explanation:

The angle is less than 45°, so you know the distance will be more than 89 feet. There is only one choice in that range.

The mnemonic SOH CAH TOA reminds you ...

... Tan = Opposite/Adjacent

so ...

... tan(30°) = (89 ft)/(distance to boat)

Then ...

... distance to boat = (89 ft)/tan(30°) ≈ 154 ft

What is the angle of depression from the top of the lighthouse to Thomas

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