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3 years ago

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Mathematics

1 answer:

otez555 [7]3 years ago

7 0

Answer:

Height of the cliff = 13.66 m

Step-by-step explanation:

Let the height of the cliff is 'x' m and distance between the base of the cliff and the boat is 'y' m.

From right triangle AOC,

tan 30° = $\frac{\text{Opposite triangle}}{\text{Adjacent side}}$

$\frac{1}{\sqrt{3}}=\frac{x}{y}$

y = $x\sqrt{3}$ ------(1)

From right angle triangle BOC,

tan 45° = $\frac{x}{y-10}$

$1=\frac{x}{y-10}$

x = y - 10

y = x + 10 -------(2)

From equations (1) and (2),

$x\sqrt{3}=x+10$

$x(\sqrt{3}-1)=10$

$x=\frac{10}{\sqrt{3}-1 }$

x = 13.66 m

Therefore, height of the cliff is 13.66 m.

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<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

y = mx also represents direct proportionality. We can write [m] as -

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We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

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Equations that represents the relationship can be written as -

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