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Mathematics

1 answer:

yarga [219]2 years ago

5 0

Answer:

Step-by-step explanation:

Angle c = 90 degrees

90 + 2x + x = 180 degrees

3x = 90

x =30 degrees

2x = 30*2 = 60 degrees

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If Randy sells 8 times as many vacuum cleaners as Janice, and Janice sells 690 vacuum cleaners per year, on average, how many do

drek231 [11]

Randy sells, in average, 460 vacuum cleaners per month.

<h3>How many vacuum cleaners does Randy sell each month?.</h3>

First, we know that Janice sells 690 units per year.

There are 12 months in a year, so the amount that she sells, in average, per month is:

J = 690/12 = 57.5

This means that Janice sells, in average, 57.5 units per month. And Randy sells 8 times as many, then we can solve the product:

R = 8*57.5 = 460

This means that Randy sells 460 units per month.

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Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle

Nina [5.8K]

The firts thig we are going to do is create tow triangles using the angles of elevation of Paul and Jose. Since the problem is not giving us their height we'll assume that the horizontal line of sight of both of them coincide with the base of the tree.
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as $x$ .
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
$cos(59)= \frac{19}{h}$
$h= \frac{19}{cos(59)}$
$h=36.9$
Now we can use the law of sines to find the distance $x$ between Paul and Jose:
$\frac{sin(43)}{36.9} = \frac{sin(16)}{x}$
$x= \frac{36.9sin(16)}{sin(43)}$
$x=14.9$

Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
$19m+14.9=33.9m$

We can conclude that Jose is 33.9m from the base of the tree.