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2 years ago

I need help!!! I don't get it.

Mathematics

1 answer:

elena-14-01-66 [18.8K]2 years ago

5 0

The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.

<h3>What are trigonometric ratios?</h3>

The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

cosec θ = hypotenuse/opposite

cot θ = adjacent/opposite

<h3>Calculation:</h3>

It is given that,

The height of the bacon-light is 135 feet above the water

Consider the horizontal distance between the boat and the lighthouse = x feet

The angle of elevation is given as 4°

Constructing a model as below in the figure.

From the trigonometric ratios, we have

tan θ = 135/x

⇒ tan 4° = 135/x

⇒ x = 135/tan 4°

∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)

Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.

Learn more about trigonometric ratios here:

brainly.com/question/24349828

#SPJ1

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2 years ago

The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at

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The formula for the area of a triangle is
$A=\frac{1}{2}bh$
$\rightarrow\frac{dA}{dt}=\frac{1}{2}(b\frac{dh}{dt}+h\frac{db}{dt})$

We are given:
$\frac{dh}{dt}=2$
$\frac{dA}{dt}=4.5$
$h=9.5$
$A=92$

Plug in:
$4.5=\frac{1}{2}(b*2+9.5\frac{db}{dt})$
We can find $b$ with:
$A=\frac{1}{2}bh\rightarrowb=\frac{2A}{h}=\frac{2*92}{9.5}=\frac{184}{9.5}$
So $4.5=\frac{1}{2}(2*\frac{184}{9.5}+9.5\frac{db}{dt})$
$\rightarrow9=\frac{368}{9.5}+9.5\frac{db}{dt}$
$\rightarrow9-\frac{368}{9.5}=9.5\frac{db}{dt}$
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