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4 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?

1 answer:

Genrish500 [490]4 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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The midpoint of segment AB is (4, 2). The coordinates of point A are (2, 7). Find the coordinates of point B.

erastovalidia [21]

Answer:

<h3>The option B) is correct</h3><h3>Therefore the coordinate of B $(x_2,y_2)$ is (6,-3)</h3>

Step-by-step explanation:

Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).

<h3>To Find the coordinates of point B:</h3>

Let the coordinate of A be $(x_1,y_1)$ is (2,7) respectively
Let the coordinate of B be $(x_2,y_2)$
And Let M(x,y) be the mid point of line segment AB is (4,2) respectively
The mid-point formula is

<h3> $M(x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ </h3>

Now substitute the coordinates int he above formula we get
$(4,2)=(\frac{2+x_2}{2},\frac{7+y_2}{2})$
Now equating we get

$4=\frac{2+x_2}{2}$ $2=\frac{7+y_2}{2}$

Multiply by 2 we get Multiply by 2 we get

$4(2)=2+x_2$ $2(2)=7+y_2$

$8=2+x_2$ $4=7+y_2$

Subtracting 2 on both

the sides Subtracting 7 on both the sides

$8-2=2+x_2-2$ $4-7=7+y_2-7$

$6=x_2$ $-3=y_2$

Rewritting the above equation Rewritting the equation

$x_2=6$ $y_2=-3$

<h3>Therefore the coordinate of B $(x_2,y_2)$ is (6,-3)</h3><h3>Therefore the option B) is correct.</h3>

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3 years ago

What is 8 times 56 and what is 7 time 14

sp2606 [1]

8*56=448 and 7*14=98

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3 years ago

Which of the following expressions represents the distance between 5/2 and 4 7/8 on a number line?

hjlf

Answer:

<h2>C. None of the above</h2>

Step-by-step explanation:

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3 years ago

The following is the formula for finding the area (A) of a trapezoid with height (h) and bases (b1) and (b2). A = 1/2h(b1 + b2)

charle [14.2K]

Answer:

<em>Correct choice: B</em>

Step-by-step explanation:

<u>Equation Solving</u>

The area of a trapezoid with height h and bases b1 and b2 is given by:

$\displaystyle A=\frac{1}{2}h(b_1+b_2)$

We must solve this formula for h.

First, multiply by 2 to eliminate denominators:

$\displaystyle 2A=h(b_1+b_2)$

Now, divide by b1+b2:

$\displaystyle \frac{2A}{b_1+b_2}=h$

Swapping sides:

$\displaystyle h=\frac{2A}{b_1+b_2}$

Correct choice: B

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3 years ago

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3 years ago

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