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motikmotik
3 years ago
15

A lighthouse keeper views a small boat at an angle of depression of 62 degrees. The boat is 446 feet away from the base of the l

ighthouse. How tall is the lighthouse?

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0

Answer: the height of the lighthouse is 838.8 feet

Step-by-step explanation:

The right angle triangle ABC illustrating the scenario is shown in the attached photo.

The angle of depression and angle A are alternate angles, hence, they are the equal.

The height, h of the lighthouse represents the opposite side of the right angle triangle. The distance of the boat from the foot of the lighthouse represents the adjacent side of the right angle triangle.

To determine h, we would apply

the tangent trigonometric ratio.

Tan θ, = opposite side/adjacent side. Therefore,

Tan 62 = h/446

h = 446tan62 = 446 × 1.8807

h = 838.8 feet to the nearest tenth.

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What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60
Amanda [17]

The answer is:  " x = 105.41 " . 

_____________________________________________

Explanation:

_____________________________________________

Given:   " 24 log (3x) = 60 " ;  Solve for "x" .

The default is to assume "base 10" for the "logarithm". 

_____________________________________________

Start by dividing each side of the equation by "24" ; 

       →   [ 24 log(3x) ] / 24  = 60 / 24 ; 

to get:  

_____________________________________________

 log (3x)  = 2.5 ;

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Rewrite as:  log₁₀ (3x) = 2.5 ;  

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Using the property of logarithms:

⇔    10⁽²·⁵⁾  =   3x  ;  

↔   3x = 10⁽²·⁵⁾   ;

         →  10^ (2.5) = 316.2277660168379332 ;

     →  3x = 316.227766016837933 ;  

Divide each side of the equation by "3" ;

  to isolate "x" on one side of the equation;

      and to solve for "x" ;

    →  3x / 3 =  316.2277660168379332 / 3  ;

to get:

    →   x = 105.4092553389459777333 ;

    →  round to 2 (two) decimal places;

_____________________________________________

         →   " x = 105.41 " .

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 Hope this helps!

    Best wishes to you!

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8 0
3 years ago
A circle has a diameter of 12 units, and its center lies on the x-axis. what could be the equation of the circle? check all that
wariber [46]

The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle has a diameter of 12 units. Hence, radius = 12/2 = 6 units.

The center of the circle is at x axis (*, 0), the equation could be:

(x - 6)² + (y - 0)² = 6²

(x - 6)² + y² = 36

The equation of a circle with radius of 6 units and center on the x axis could be (x - 6)² + y² = 36

Find out more on equation at: brainly.com/question/2972832

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5 0
2 years ago
Factor Completely: x2 - 81 <br> A.(x-9)(x+9)<br> B.(x+9)(x+9)<br> C.(x-9)(x-9)<br> D.(9-x)(9+x)
Hunter-Best [27]

Answer is A

The binomial can be factored using the difference of squares formula a2-b2 = (a+b) (a-b) where a=x and b=9

(X+9) x(x-9)

7 0
3 years ago
Read 2 more answers
I need to know how to solve these
My name is Ann [436]
1. make an equation
4x+7(20) = 5(x+20)
2. multiply the numbers and distribute 5 through the parenthesis
4x+140 = 5x+100
3. move variables to the left side and change its sign and move constant to the right side and change its sign
4x-5x = 100-140
4. collect the like terms and calculate the difference
-x = -40
5. change the signs on both sides of the equation
x = 40
he needs to use 40 pounds of the cheaper coffee.
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4 0
2 years ago
Mike has $6000 to invest. He invested part of his total into an account earning 6% interest and the rest in an account earning 1
lesya692 [45]

Answer:$4000 was invested into the account earning 6% interest.

$2000 was invested into the account earning 11% interest.

Step-by-step explanation:

Let x represent the amount invested into the account earning 6% interest.

Let y represent the amount invested into the account earning 11% interest.

Mike has $6000 to invest. He invested part of his total into an account earning 6% interest and the rest in an account earning 11% interest. This means that

x + y = 6000

The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

Considering the account earning 6% interest, the interest would be

I = (x × 6 × 1)/100 = 0.06x

Considering the account earning 11% interest, the interest would be

I = (x × 11 × 1)/100 = 0.11y

If at the end of the year, he earned $460.00 in interest, it means that

0.06x + 0.11y = 460 - - - - - - - - - - -1

Substituting x = 6000 - y into equation 1, it becomes

0.06(6000 - y) + 0.11y = 460

360 - 0.06y + 0.11y = 460

- 0.06y + 0.11y = 460 - 360

0.05y = 100

y = 100/0.05 = $2000

x = 6000 - y = 6000 - 2000

x = $4000

3 0
3 years ago
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