1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kherson [118]
3 years ago
14

The length of a shadow from the vertical pole (see picture to the right), which is 7m high, is 4m. What is the degree measure of

the sun above the horizon?
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0

Answer:

The answer to your question is:  60.3°

Step-by-step explanation:

Data

height = 7 m

shadow = 4 m

angle = ?

Process

tangent Ф = opposite side / adjacent side

tangent Ф = 7 / 4

tan Ф = 1.75

     Ф = 60.3°

You might be interested in
A 12-meter ladder leans against a building forming a 30° angle with the building.
KatRina [158]

Answer:

will show you two (2) ways to solve this problem.

A diagram is needed to see what is going on....

 

Without loss of generality (WLOG)

The wall is on the right. The ladder leans against the wall

with a POSITIVE slope, from SW to NE (quadrant 3 to quadrant 1).

The measure from the bottom of the ladder to the wall is 6.

 

 

Option 1:

 

The ladder, ground and wall form a right triangle.

 

The hypotenuse (ladder) is 14 feet.

 

 The bottom of the ladder is 6 feet from the wall,

  so the base of this right triangle is 6 feet.

 

The top of the ladder to the ground represents

the missing leg of the right triangle.

 

The pythagorean theorem applies, which says

 6^2 + h^2 = 14^2   where h is the height

                                 of the top of the ladder to the ground

 

36 + h^2 = 196

 

 h^2 = 196 - 36

 

h^2  = 160

 

h = sqrt(160)

 

   = sqrt(16 * 10)

 

    = sqrt(16)* sqrt(10)

 

    = 4*sqrt(10) <--- exact answer

 

    = 4 * 3.16227766016838....

 

     = 12.64911....

 

    12.65 <--- rounded to 2 digits as directed

 

----------------------------------------------

Option #2: using trig

 

With respect to the angle formed by the bottom of the

ladder with the ground

  cos T = 6/14 = 3/7  

 T = inverse-cosine(3/7) = 64.623006647 degrees

 

 sin(64.623006647) = h/14

 

 h = 14*sin(64.62300647) = 12.6491106 <--- same answer                        

hope this helps

Step-by-step explanation:

5 0
2 years ago
Prove the following statements: (a) For every integer x, if x is even, then for every integer y, xy is even. (b) For every integ
Murrr4er [49]

Answer and Step-by-step explanation:

(a) Given that x and y is even, we want to prove that xy is also even.

For x and y to be even, x and y have to be a multiple of 2. Let x = 2k and y = 2p where k and p are real numbers. xy = 2k x 2p = 4kp = 2(2kp). The product is a multiple of 2, this means the number is also even. Hence xy is even when x and y are even.

(b) in reality, if an odd number multiplies and odd number, the result is also an odd number. Therefore, the question is wrong. I assume they wanted to ask for the proof that the product is also odd. If that's the case, then this is the proof:

Given that x and y are odd, we want to prove that xy is odd. For x and y to be odd, they have to be multiples of 2 with 1 added to it. Therefore, suppose x = 2k + 1 and y = 2p + 1 then xy = (2k + 1)(2p + 1) = 4kp + 2k + 2p + 1 = 2(kp + k + p) + 1. Let kp + k + p = q, then we have 2q + 1 which is also odd.

(c) Given that x is odd we want to prove that 3x is also odd. Firstly, we've proven above that xy is odd if x and y are odd. 3 is an odd number and we are told that x is odd. Therefore it follows from the second proof that 3x is also odd.

3 0
3 years ago
There are 6 showings of a film about Van Gogh at the art museum. A total of 459 people saw the film. The same number of people w
Strike441 [17]

Answer:

548

Step-by-step explanation:

its obvious

8 0
3 years ago
What is 4 divided by 84? I don't understand how you get 21?
Romashka [77]
<span>What is 4 divided by 84? 

4 </span>÷ 84 = <span>0.04761904761....

4 divided by 84 isn't 21, but 84 divided by 4 is 21! 4 divided by 84 is asking how many times 84 goes into 4 which is not even 1.
</span>
 4 divided by 84 = <span>0.04761904761....</span>
4 0
3 years ago
The volume of a cylinder is 81 pi in^3 and the height of the cylinder is 1 in. What is the radius of the​ cylinder
ladessa [460]

Answer:

18/20π

Step-by-step explanation:

81π ÷ 1 = 81π

81π ÷2 = 18/20π

You do this because the radius is half of the diameter and you need to get rid of the hight by dividing it from the volume.

7 0
2 years ago
Other questions:
  • 1.
    6·2 answers
  • Write the polynomial function with the given zeros.<br> 5. x= -1,-1, 6
    14·1 answer
  • How to understand piecewise functions
    10·1 answer
  • The ratio of boys to girls in a school is 5:8.If the number of girls exceeds the number of boys by 144, calculate the total numb
    14·1 answer
  • An oral surgeon is tracking how many patients were referred to him by various local dentists. In the past year, 5 dentists made
    7·2 answers
  • Match the inequality to the graph of its solution.
    7·1 answer
  • Matrix tossed three coines wat is the probability that all three coins will land on the same side
    12·1 answer
  • A triangle has angles that measure 55°, 53°, and 72°. What kind of triangle is it?
    7·1 answer
  • Which graph represents the solution to the system of inequalities?
    6·1 answer
  • Solve for x. please explain in detail
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!