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11Alexandr11 [23.1K]
3 years ago
9

A pilot in an apache rescue helicopter, at an altitude of 1200 feet, spots his two soldiers on the ground. the angles of depress

ion to the soldiers are 53 and 30. How far apart are the two soldiers, to the nearest foot

Mathematics
1 answer:
kykrilka [37]3 years ago
6 0

Answer:

x=1174\ feet

Step-by-step explanation:

<u>Right Triangle </u>

It's a special type of triangle where one of its internal angles is 90°. The basic trigonometric formulas apply to relate lengths and angles. If h is the opposite side to the angle \theta, and x is the adjacent side of the same angle, then

\displaystyle tan\theta =\frac{h}{x}

Or, equivalently

\displaystyle x =\frac{h}{tan\theta}

The helicopter, ground and the two soldiers form two right triangles, as shown in the image below. Let's call x1 the distance from soldier 1 to the point O, then

\displaystyle x_1 =\frac{h}{tan53^o}

\displaystyle x_1 =\frac{1200}{tan53^o}

x_1=904 \ feet

Now for x2, the distance from soldier 2 to the point O

\displaystyle x_2 =\frac{1200}{tan30^o}

x_2=2078\ feet

The distance between the soldiers is  

x=2078\ feet-904\ feet

\boxed{x=1174\ feet}

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Answer:

Step-by-step explanation:

Let the first number = x

Let the second number = x + 9

Let the third number = 4x

Together they make 123

x + x + 9 + 4x = 123              combine the left

6x + 9 = 123                         Subtract 9 from both sides

6x = 123 - 9

6x = 114                                 Divide by 6

x = 114/6

x = 19

=================

First number = 19

Second number = 19 + 9 = 28

Third number = 4*19 = 76

8 0
3 years ago
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
zalisa [80]

Answer: 272

Step-by-step explanation:

Let a1=11

a2=20

a3=29

Formula for sequence=

an=a1+(n-1)d

an = nth term

a1= first term

n= nth position

d= common difference

We are looking for the 30th term,so our n=30

d= a2-a1

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Using the formula

an= a1+(n-1)d

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Adina read 60 out of 100 pages in a comic book.Write the fraction of the pages she read in simplest form
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Answer:

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Step-by-step explanation:

60 divided by 20 is 3 and 100 divided by 20 is 5.

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Answer:

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General Formulas and Concepts:

<u>Algebra I</u>

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Step-by-step explanation:

The solution set to any systems of equations is where the 2 lines intersect. According to the graph, we see that the 2 lines intersect at (-3, 5). Therefore, our answer is A.

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Answer:

Step-by-step explanation:

Equation of blue line:

blue line is parallel to y-axis

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Equation of green line:

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y = 2

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