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vazorg [7]
3 years ago
13

Find the angle of depression from the top of a lighthouse, 260 feet above water to a ship that's 270 feet offshore?

Mathematics
1 answer:
expeople1 [14]3 years ago
4 0

Answer: OPTION C.

Step-by-step explanation:

Observe the triangle ABC attached.

Notice that the angle of depression is represented with \alpha.

Knowing that the top of a lighthouse is 260 feet above water and the ship is 270 feet offshore, you can find the value of  \alpha by using arctangent:

\alpha= arctan(\frac{opposite}{adjacent})

In this case you can identify that:

opposite=260\\adjacent=270

Therefore, substuting values into  \alpha= arctan(\frac{opposite}{adjacent}), you get that the angle of depression is:

 \alpha= arctan(\frac{260}{270})\\\\\alpha=43.92\°

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The first row of seats in Section G of a baseball stadium has 5 seats . There is a total of 20 rows of seats in the section . If
RoseWind [281]

Answer:

140

Step-by-step explanation:

8 0
3 years ago
A circle's radius is 14 centimeters.
spayn [35]

Answer:

Circumference of circle = 87.92 centimeter

Step-by-step explanation:

In the given question;

Radius of circle = 14 centimeters

Value of π = 3.14

Find:

Circumference of circle

Computation:

⇒ Circumference of circle = 2πr

where r = Radius of circle

⇒ Circumference of circle = 2(3.14)(14)

⇒ Circumference of circle = (6.28)(14)

Circumference of circle = 87.92 centimeter

4 0
3 years ago
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underw
Serggg [28]

Answer:

b = 0.0138

Step-by-step explanation:

Given

Regression Equation:

DD=2.69+0.0138D

Required

Determine the slope of the regression line

The equation of regression is of the form

Y =  a + bX

Where b represents the slope;

Compare Y =  a + bX to the given equation

DD=2.69+0.0138D

We have that:

Y = DD

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X = D

Hence; the slope is:

b = 0.0138

7 0
3 years ago
Please help need answer!
never [62]

Answer:  About 513 feet

A more accurate value is roughly 512.575960394824

==============================================================

Explanation:

With many trig problems, a diagram should help steer you in the right direction. See below.

The red angle is the angle of depression. It's formed by starting off looking straight horizontal, then we look down 26 degrees. The blue angle adds to the red angle to get 90, so we can see that 26+64 = 90. Or you could say 90-26 = 64.

The goal is to find the value of x, which is the length from B (the lighthouse base) to point C (the ship's location).

The lighthouse is 250 ft tall, meaning AB = 250

We'll use angle BAC, or angle A for short, as the reference angle. This is the blue angle in the diagram.

We have a known adjacent side (AB = 250) and an unknown opposite side (BC = x). We use a tangent ratio to tie these sides together with the reference angle in question. This way we can solve for x.

-------------------

tan(angle) = opposite/adjacent

tan(A) = BC/AB

tan(64) = x/250

250*tan(64) = x

x = 250*tan(64)

x = 512.575960394824

x = 513

The distance from B to C is roughly 513 feet.

I'm rounding to the nearest whole number because the other values given to you are whole numbers.

7 0
3 years ago
PLEASE HELP ASAP!!!! 50 POINTS!!
Kamila [148]

Answer:

Hope this helps!!

Step-by-step explanation:

2ya and 2yb where a and b have no common factors and a and b are polynomaals

a=(x+2)(x+3)

b=(x+4)(x+5)

no common factors betwen a and b

so

2ya=2y(x+2)(x+3)=2yx²+10xy+12y

2yb=2y(x+4)(x+5)=2yx²+18xy+40y

the 2 polynomials  are  2yx²+18xy+40y and 2yx²+10xy+12y

4 0
3 years ago
Read 2 more answers
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