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3 years ago

7

karie builds a skate ramp with 2 metres of wood. she wants the vertical height of the ramp to be 1 metre. what does the angle el

evation need to be

1 answer:

MA_775_DIABLO [31]3 years ago

4 0

9514 1404 393

Answer:

30°

Step-by-step explanation:

The relationship between triangle sides and angles can be remembered using the mnemonic SOH CAH TOA. Here, we're interested in the relationship involving the hypotenuse and the side opposite the angle:

Sin = Opposite/Hypotenuse

For a ramp 1 m high and 2 m long, we have ...

sin(x) = (1 m)/(2 m) = 1/2

x = arcsin(1/2) = 30°

The elevation angle of the ramp needs to be 30°.

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Read 2 more answers

The point slope form of the equation of the line that passes through (-5-1) and (10.-7) is

Natalka [10]

Answer:

The standard form of the equation for this line can be:

l: 2x + 5y = -15.

Step-by-step explanation:

Start by finding the slope of this line.

For a line that goes through the two points $(x_0, y_0)$ and $(x_1, y_1)$ ,

$\displaystyle \text{Slope} = \frac{y_{1} - y_{0}}{x_{1} - x_{0}}$ .

For this line,

$\displaystyle \text{Slope} = \frac{(-1) - (-7)}{(-5) - 10} = -\frac{2}{5}$ .

Find the slope-point form of this line's equation using

$\displaystyle \text{Slope} = -\frac{2}{5}$ , and
The point $(-5, -1)$ (using the point $(10, -7)$ should also work.)

The slope-point form of the equation of a line

with slope $m$ and
point $(x_{0}, y_{0})$

should be $l:\; y - y_{0} = m(x - x_0)$ .

For this line,

$\displaystyle m = -\frac{2}{5}$ , and
$x_0 = -5$ , and
$y_0 = -1$ .

The equation in slope-point form will be

$\displaystyle l:\; y - (-1) = -\frac{2}{5}(x - (-5))$ .

The standard form of the equation of a line in a cartesian plane is

$l: \; ax + by = c$

where

$a$ , $b$ , and $c$ are integers. $a \ge 0$ .

Multiply both sides of the slope-point form equation of this line by $5$ :

$l:\; 5 y + 5 = -2x -10$ .

Add $(2x-5)$ to both sides of the equation:

$l: \; 2x + 5y = -15$ .

Therefore, the equation of this line in standard form is $l: \; 2x + 5y = -15$ .

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3 years ago