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
lianna [129]
3 years ago
6

The tallest tree in the world is reputed to be a giant redwood named Hyperion located in Redwood National Park in California, US

A. At a point 41.5 meters from the centre of its base and on the same elevation, the angle of elevation of the top of the tree is 70°. How tall is the tree?
Mathematics
1 answer:
dlinn [17]3 years ago
5 0

Answer:

114.02 meters

Step-by-step explanation:

The information you're given about the tree will form a triangle, with the three corners being the top of the tree, the point where the tree meets the ground, and the specified point 41.5 meters from the tree. The angle of elevation (70°) is the angle made where the line representing the ground and the line connecting the top of the tree to the ground at the specified point connect.

The angle where the tree meets the ground is 90°, so the triangle a right triangle.

So this all means you know one angle of a right triangle (70°) and the side adjacent to this angle (41.5 meters). You're solving for the height of the tree, which is the side opposite of the angle you know. You can solve using either <em>Sine, Cosine, </em>or <em>Tangent.</em>

Use the acronym SOHCAHTOA to figure out which of those three functions to use. Feel free to look this up for more information if you haven't heard of it before. In this case, we're using Tangent (TOA = Tangent, Opposite side, Adjacent side)

To solve using any of those three functions, you'll need a scientific calculator. On your calculator, you'll see the buttons <em>SIN, COS, </em>and<em>TAN.</em> For this problem, press <em>TAN</em> and you'll see something appear that says <em>tan (___)</em>. You'll need to input a number to get your answer, and here's how to find that number:

Again referencing SOHCAHTOA, the "TOA" part lists Opposite first and then Adjacent. This is because you're going to write a fraction with those two numbers, and since Opposite is first, it's the numerator. That means that Adjacent is the denominator. We don't know the value of the opposite side, so it'll be represented by <em>x</em>, and we do know the value of the adjacent side, 41.5. This means the fraction is \frac{x}{41.5} .

This isn't the number to input into the calculator -- you need to isolate the variable:

The original equation is:

tan 70 = x/41.5

Multiply both sides by 41.5 (To cancel out the denominator and isolate <em>x</em>)

tan 70 (41.5) = x

Now you've got the equation for <em>x, </em>you're ready to put this in your calculator.

What appeared on your calculator was:

tan(__)

Input like follows:

(tan(70))41.5

The brackets are needed like that so the calculator knows to multiply the entire thing by 41.5. You might get a wrong answer otherwise.

Hit enter, and you'l get the height of the tree:

114.02 meters

You might be interested in
A student broke this trapezoid into two triangles. She says she has enough information to find the area of it. Is she correct? E
forsale [732]
It depends on what measurements are given. Do you have a photo? Please revise your question
6 0
3 years ago
Read 2 more answers
How do you spin the spinner 66 times what is the theoretical probability of it landing on on a odd number
MrRa [10]

Answer:

A CIRCLE

Step-by-step explanation:

ITS A BALL AND IT SPINS CAUSE IT HAS NO SIDES TO STOP

4 0
3 years ago
Do you tailgate the car in front of you? About 35% of all drivers will tailgate before passing, thinking they can make the car i
Vesna [10]

Answer:

(a) The histogram is shown below.

(b) E (X) = 4.2

(c) SD (X) = 2.73

Step-by-step explanation:

Let <em>X</em> = <em>r</em><em> </em>= a driver will tailgate the car in front of him before passing.

The probability that a driver will tailgate the car in front of him before passing is, P (X) = <em>p</em> = 0.35.

The sample selected is of size <em>n</em> = 12.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 12 and <em>p</em> = 0.35.

The probability function of a binomial random variable is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x}

(a)

For <em>X</em> = 0 the probability is:

P(X=0)={12\choose 0}(0.35)^{0}(1-0.35)^{12-0}=0.006

For <em>X</em> = 1 the probability is:

P(X=1)={12\choose 1}(0.35)^{1}(1-0.35)^{12-1}=0.037

For <em>X</em> = 2 the probability is:

P(X=2)={12\choose 2}(0.35)^{2}(1-0.35)^{12-2}=0.109

Similarly the remaining probabilities will be computed.

The probability distribution table is shown below.

The histogram is also shown below.

(b)

The expected value of a Binomial distribution is:

E(X)=np

The expected number of vehicles out of 12 that will tailgate is:

E(X)=np=12\times0.35=4.2

Thus, the expected number of vehicles out of 12 that will tailgate is 4.2.

(c)

The standard deviation of a Binomial distribution is:

SD(X)=np(1-p)

The standard deviation of vehicles out of 12 that will tailgate is:

SD(X)=np(1-p)=12\times0.35\times(1-0.35)=2.73\\

Thus, the standard deviation of vehicles out of 12 that will tailgate is 2.73.

4 0
3 years ago
One number is twelve greater than another number. Twice the larger plus five times the smaller is 38. Find both numbers.
SSSSS [86.1K]

Answer:

I need points because i have a question

Step-by-step explanation:

And i need major help hope u understand also thanks

8 0
3 years ago
Pythagorean Theorem
tatiyna
The answer is 10.6 :)
8 0
1 year ago
Read 2 more answers
Other questions:
  • Daria's goal to run 7 miles each weekend.She ran 3 1/3 miles on sturday and 3 3/4 miles on sunday.by how much did she beat her g
    15·1 answer
  • Work out the area of a triangle of base 7.5m And height 6cm! <br> Please and thanks beforehand!❤️
    13·1 answer
  • Find the product. (-3ab 2)3
    6·2 answers
  • ThE product of two numbers is 20 . if one the numbers is 6 1/4 what is the other number
    10·1 answer
  • The value of the surface area (in square centimeters) of the cone is equal to the value of the volume (in cubic centimeters) of
    9·1 answer
  • The value of Maggie's car decreased by 20% since last year, when she bought it. If the car is now worth $15,000.00, how much was
    15·1 answer
  • Point Q is the image of Q(-7,-6) under the translation (,y) → (x + 12, y +8) <br><br> Answer: (5,2)
    12·1 answer
  • A simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard de
    7·2 answers
  • What is 235 times 1000
    11·2 answers
  • The graph of a function is shown.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!