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lakkis [162]
3 years ago
11

In ΔKLM, m = 5.3 inches, ∠K=21° and ∠L=88°. Find the length of k, to the nearest 10th of an inch.

Mathematics
1 answer:
gtnhenbr [62]3 years ago
6 0

Answer:

20.9 ft

Step-by-step explanation:

This is a right triangle trigonometry question because N is 90 degrees. MN is adjacent to M and LM is the hypotenuse. Adjacent any hypotenuse use the cosine function. 

plug in known values

switch cos(20) and x using the products property

plug into calculator to get 20.9 ft

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Answer:             1/10 miles/hour

To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.

<h2>Unit Rate</h2>

The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.

<h2>Proportions</h2>

Proportions look like two fractions set equal to each other with a missing variable to solve.

<h3>State our variables</h3>

let <em>x</em> be the number of miles per hour

<h3>Write a proportion</h3>

The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}

<h2>Solve</h2>

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.

<h3>Find the scale factor</h3>

Start with the proportion.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}

To find the scale factor,

  1. Take the denominator from the fraction with a variable: 1\ hr
  2. Take the denominator from the fraction that has no variable:  \frac{1}{3}\ hr
  3. Divide step 1 by step 2 and solve:  1\ hr\ \div\ \frac{1}{3}\ hr = 3

Our scale factor is <u>3</u>.

<h3>Solve for x</h3>

We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}

Simplify 3/30 by dividing the fraction by 3.

\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}

x = 1/10

∴ a snail moves 1/10 miles per hour.

Learn another way to solve proportions here: brainly.com/question/18437927

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