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Sauron [17]
3 years ago
11

You have climbed to the top of a tall tree. When you get to the top, you use your clinometer to discover that the angle between

the tree and the line of sight to your red lunchbox is 30°. You know you left the lunchbox 20 meters from the base of the tree. How tall is the tree?
A. 75.36 m
B. 92.09 m
C. 20.17 m
D. 51.25 m
E. 18.95 m
F. 34.64 m

Mathematics
1 answer:
GuDViN [60]3 years ago
5 0

Answer:

F. 34.64 m

Step-by-step explanation:

The measurements given in the question are;

The angle (of depression) given by the clinometer, θ = 30°

The horizontal distance of the lunchbox from the tree, d = 20 meters

The height (how tall) of the tree = Required

Let the height of the tree be assumed to be perpendicular to the ground, noting that the horizontal distance from the lunchbox to the tree is a straight line, let <em>l</em> represent the line of sight from the top of the tree to the lunchbox, and let <em>h </em>represent the height of the tree we have;

The line of sight to the lunchbox, <em>l</em>, the height of the tree, <em>h</em>, and the horizontal distance of the lunchbox from the base of the tree form a right triangle

The height of the tree is the adjacent leg to the given angle by the clinometer

Using trigonometric ratios, we have;

tan(30°) = d/h

∴ tan(30°) = (20 m)/h

h = (20 m)/tan(30°) ≈ 34.64m

The height of the tree, h ≈ 36.64 m.

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3 years ago
Factor completely.<br> 16n^6+40n^3+25
Andru [333]

Answer:Step  1  :

Equation at the end of step  1  :

 ((16 • (n6)) +  (23•5n3)) +  25

Step  2  :

Equation at the end of step  2  :

 (24n6 +  (23•5n3)) +  25

Step  3  :

Trying to factor by splitting the middle term

3.1     Factoring  16n6+40n3+25

The first term is,  16n6  its coefficient is  16 .

The middle term is,  +40n3  its coefficient is  40 .

The last term, "the constant", is  +25

Step-1 : Multiply the coefficient of the first term by the constant   16 • 25 = 400

Step-2 : Find two factors of  400  whose sum equals the coefficient of the middle term, which is   40 .

     -400    +    -1    =    -401

     -200    +    -2    =    -202

     -100    +    -4    =    -104

     -80    +    -5    =    -85

     -50    +    -8    =    -58

     -40    +    -10    =    -50

     -25    +    -16    =    -41

     -20    +    -20    =    -40

     -16    +    -25    =    -41

     -10    +    -40    =    -50

     -8    +    -50    =    -58

     -5    +    -80    =    -85

     -4    +    -100    =    -104

     -2    +    -200    =    -202

     -1    +    -400    =    -401

     1    +    400    =    401

     2    +    200    =    202

     4    +    100    =    104

     5    +    80    =    85

     8    +    50    =    58

     10    +    40    =    50

     16    +    25    =    41

     20    +    20    =    40    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  20  and  20

                    16n6 + 20n3 + 20n3 + 25

Step-4 : Add up the first 2 terms, pulling out like factors :

                   4n3 • (4n3+5)

             Add up the last 2 terms, pulling out common factors :

                   5 • (4n3+5)

Step-5 : Add up the four terms of step 4 :

                   (4n3+5)  •  (4n3+5)

            Which is the desired factorization

Trying to factor as a Sum of Cubes :

3.2      Factoring:  4n3+5

Theory : A sum of two perfect cubes,  a3 + b3 can be factored into  :

            (a+b) • (a2-ab+b2)

Proof  : (a+b) • (a2-ab+b2) =

   a3-a2b+ab2+ba2-b2a+b3 =

   a3+(a2b-ba2)+(ab2-b2a)+b3=

   a3+0+0+b3=

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Check :  4  is not a cube !!

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