All categories

3 years ago

The following figure is drawn to find the distance across a lake, CD.

Mathematics

1 answer:

Aloiza [94]3 years ago

7 0

Hello!

To do this, we know the two triangles are similar, so we can set up a proportion, and then find the length of the lake.

----

The two triangles (Triangle AEB and ADC) are similar. We know this because all the angles have the same measurement - They all share angle A, they both have a right angle, and therefore, their third angle measures the same.

What we know about both triangles is their hypotenuse length. We know that triangle AEB has a hypotenuse that measures 320 m, and ADC has a hypotenuse that measures 320 + 162, or 482 m.

320 : 482 is therefore the ratio between the side lengths of two triangles (AEB : ADC). We can simplify this to 160 : 241.

Now, what we are looking for is the side length DC. The corresponding side to this in triangle AEB is EB, and we know it measures 40 m. Therefore, using the ratio, we can find the measure of DC.

160 / 4 : 241 / 4

40 : 60.25

Therefore, the measure of DC is 60.25 m.

----

Hope this helps!

You might be interested in

What inequality is graphed below? x > 7 x ≤ 7 x < 7 x ≥ 7

Wittaler [7]

Answer:

x < 7

Step-by-step explanation:

The hollow circle represents less than or greater than. Because the arrow points to the left, the line is representing less than.

4 0

4 years ago

295.6 divided by 10 with the power of 2

stealth61 [152]

Answer:

2.956

Step-by-step explanation:

$\frac{295.6}{10^2}$

= $\frac{295.6}{100}$

= 2.956

6 0

3 years ago

Read 2 more answers

What is 18:14 equal to

skad [1K]

It equals 9:7
If its the answer u want

3 0

3 years ago

a hiking path is represented by the equation y=3/8x on a coordinate map. The county would like to create a parallel path for bik

stepladder [879]

Answer:

The equation of the bike path on a coordinate map is represented by $y = \frac{3}{8}\cdot x +1$ .

Step-by-step explanation:

From Analytical Geometry, we know that resultant parallel line is a translated version of parent line. Two lines are parallel to each other when they share the same slope. The resultant line can be construted from slope-point form:

$y-y_{o} = m_{\parallel}\cdot (x-x_{o})$

Where:

$x_{o}$ , $y_{o}$ - Components of known point, dimensionless.

$m_{\parallel}$ - Slope of the parallel line, dimensionless.

In addition, a line has also this form:

$y = m\cdot x + b$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$m$ - Slope, dimensionless.

$b$ - y-Intercept, dimensionless.

Given that parent function is $y = \frac{3}{8}\cdot x$ , the slope of the resulting line is $m_{\parallel} = \frac{3}{8}$ . Now, if $x_{o} = 16$ and $y_{o} = 7$ , we obtain the equation of the line: