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Sholpan [36]
3 years ago
5

A man, 1.5m tall, is on top of a building. He observes a car on the road at an angle of 75°. If the building is 30m, how far is

the car from the building?​
Mathematics
1 answer:
kolbaska11 [484]3 years ago
6 0

Answer:

The answer to this question is 8.44 m.

Step-by-step explanation:

This problem is best illustrated in the photo below.

First, we must know that the angle stated in the problem is the angle of depression. Angle of depression is the angle between the horizontal and the line of sight of the observer. On the other hand, if the observer is looking upward, then the angle between the horizontal and his line of sight is called the angle of elevation.

Since we have the given angle of depression, we must use its complementary angle to solve for the distance of the car from the building.

Let x = complementary angle of 75°

y = distance of the car from the building

To solve for x,

To solve for y, we need to use a trigonometric function that will relate the adjacent of 15° and the opposite of 15°. Let us look at the mnemonics

SOH: Sine =  

CAH: Cosine =  

TOA: Tangent =  

Therefore we must use the tangent function to solve for y.

 

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The height of a hill, h(x), in a painting can be written as a
matrenka [14]

Answer:

First option: 6\ inches

Step-by-step explanation:

<h3> The complete exercise is: "The height of a hill, h(x), in a painting can be written as a function of x, the distance from the left side of the painting. Both h(x) and x are measured in inches h(x) = -\frac{1}{5}(x)(x -13). What is the height of the hill in the painting 3 inches from the left side of the picture?</h3>

You have the following function provided in the exercise:

h(x) = -\frac{1}{5}(x)(x -13)

You know that h(x) represents the height of the hill (in inches) and "x" represents the distance from the left side of the painting (in inches)

Knowing that you can determine that, if the painting 3 inches from the left side of the picture, the value of "x" is the following:

x=3

Therefore, you need to find the value of   h(x) when  x=3 in order to solve this exercise.  

So, the next step is to substitute  x=3 into the function:

h(x) = -\frac{1}{5}(3)(3 -13)

And finally, you must evaluate in order to find h(3).

You get that this is:

h(3) = -\frac{1}{5}(3)(-10)\\\\h(3) = -\frac{1}{5}(-30)\\\\h(3)=6

4 0
3 years ago
Read 2 more answers
1.)Find the height of a rectangular prism if the surface area is 148 cm2, the width is 4 cm and the length is 5 cm.
Contact [7]
1) surface of a rectangular prism=2(length x width)+2(length x height)+2(width x height)

Therefore:
148 cm²=2(5 cm x 4 cm)+2(5 cm x h)+2(4 cm x h)=
148 cm²=40 cm²+10 cm h+8 cm h
18 cm h=148 cm²-40 cm²
18 cm h=108 cm²
h=108 cm² / 18 cm=6 cm.

answer: height=6 cm 

2)
Volume of a rectangular prism= length x width x height 
therefore:
34 cm³=(1.7 cm)(0.5 cm) h
0.85 cm² h=34 cm³
h=34 cm³/0.85 cm²
h=40 cm.

answer: height=40 cm

3)
volume of a cylinder: πr²h
therefore.
118.79 ft³=πr²(5 ft)
r=√(118.79 ft³/5π ft)≈2.75 ft

answer: radius=2.75 ft

4)
 
Surface area of the pyramid with square base=4(A side)+A base
A side=(1/2)(8ft)(12 ft)=48 ft²
A base=(8 ft)(8 ft)=64 ft²

surface area=4(48 ft²)+64 ft²=256 ft²

Answer: the surface area of this pyramid would be 256 ft².

5)
surface of a cone=πrs+πr²
therefore:
radius=diameter/2=6.2 ft/2=3.1 ft
63.3 ft²=π(3.1 ft) s+π(3.1 ft)²
3.1π ft s=33.109 ft²
s=33.109 ft² /3.1π ft
s≈3.4 ft

Answer: the slant height would be 3.4 ft.

6)
volume of a square pyramid=(area of base x heigth)/3
therefore:
area of base=(6 ft)(6 ft)=36 ft²
126.97 ft³=36 ft² h /3
h=126.97 ft³/12 ft²=10.58 ft

answer: the height would be 10.58 ft.

7)
volume of a cone =(base x height)/3
base of a cone=πr²
therefore: 
199.23 cm³=πr²(9 cm)/3
r=√(199.23 cm³ / 3π cm)≈4.6 cm

answer: the radius would be 4.6 cm.

5 0
3 years ago
Please answer this its for 50 whole points
svlad2 [7]

Answer:

its c

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Solve for x..........................
Lelechka [254]

Answer:

3

Step-by-step explanation:

If your talking about the x where it says 3x in, then

3x = 9

x = 3

4 0
3 years ago
The product of 9 and m is 45
Jlenok [28]
9m = 45
m = 45/9 = 5.
4 0
3 years ago
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