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
bagirrra123 [75]
3 years ago
12

There is a lightning rod on top of a building. From a location 500 feet from the base of the building, the angle of elevation to

the top of the building Is measured to be 36 degrees. From the same location, the angle of elevation to the top of the lightning rod is measured to be 38 degrees. Find the height of the lightning rod. Round to the nearest foot.
Mathematics
1 answer:
Kitty [74]3 years ago
5 0
<h2>Hello!</h2>

The answer is:

The height of the  lightning rod is 27.4 feet.

<h2>Why?</h2>

To solve the problem, we need to use the given information about the two points of observation, since both are related (both finish and start at the same horizontal distance) we need to write to equations in order to establish a relationship.

So, writing the equations we have:

We know that the angle of elevation from the base of the buildings is 36°

Also, we know that from the same location, the angle of elevation to the top of the lightning rod is 38°.

Using the information we have:

To the top of the building:

tan(\alpha )=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}

To the top of the lightning rod:

tan(\alpha )=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}

Now, isolating we have:

tan(36\°)=\frac{DistanceToTheTopOfTheBuilding}{BuildingBase}\\\\DistanceToTheTopOfTheBuilding=tan(36\°)*BuildingBase \\\\DistanceToTheTopOfTheBuilding=tan(36\°)*500feet=363.27feet

Also, we have that:

tan(38\°)=\frac{DistanceToTheTopOfTheLightningRod}{BuildingBase}\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*BuildingBase\\\\DistanceToTheTopOfTheLightningRod=tan(38\°)*500feet=390.64feet

Therefore, if we want to calculate the height of the lightning rod, we need to do the following:

Let "x" the distance to the top of the building and "y" the distance to the top of the lightning rod, so:

LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet

Rounding to the nearest foot, we have:

LightningRodHeight=y-x=390.64feet-363.27feet=27.37feet=27.4feet

Hence, the answer is:

The height of the lightning rod is 27.4 feet.

Have a nice day!

You might be interested in
In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a
Softa [21]

Answer:

95% Confidence interval = (23.4,26.2)

Step-by-step explanation:

In this problem we have to develop a 95% CI for the mean.

The sample size is n=49, the mean of the sample is M=24.8 and the standard deviation of the population is σ=5.

We know that for a 95% CI, the z-value is 1.96.

The CI is

M-z*\sigma/\sqrt{n}\leq\mu\leq M+z*\sigma/\sqrt{n}\\\\24.8-1.96*5/\sqrt{49}\leq\mu\leq 24.8+1.96*5/\sqrt{49}\\\\ 24.8-1.4\leq\mu\leq 24.8+1.4\\\\23.4\leq\mu\leq 26.2

5 0
3 years ago
How does adding a solute ( use only one - salt or sugar) effect the time of water to change from a liquid to a solid?
Kruka [31]

Answer:

adding salt makes the water freeze slower and evaporate slower too.

Step-by-step explanation:

While pure water freezes at 0°C (32°F), salt water needs to be colder before it freezes and so it usually takes longer to freeze. The more salt in the water, the lower the freezing point.

4 0
3 years ago
Rearrange x - y + 1 = 0
Deffense [45]

Answer:

y=x+1

or x=y-1

Step-by-step explanation:

5 0
2 years ago
8tbsp. 2tsp.<br> x 15<br> _________
uysha [10]
The answer is 130 tablespoons
3 0
2 years ago
2/3 divided by 7/12<br> PLSLSLSLSLSLLSLSL
GarryVolchara [31]

Answer:

0.00793650794 or 8/7 in fraction form

Step-by-step explanation:

Find the reciprocal of the divisor

5 0
3 years ago
Other questions:
  • 14.Write an equation of the line that passes through (2, 7)(2, 7) and (0, −5)
    7·1 answer
  • How many tablespoons are in 1 pint
    5·2 answers
  • Hector is visiting a cousin who lives 350 miles away. He has driven 90 miles. How many more miles does he need to drive to reach
    15·2 answers
  • (m-12)(m+5)=0 <br> how do you solve it ?
    12·1 answer
  • For the quadratic equation, state the axis of symmetry, vertex, and any intercepts.
    7·1 answer
  • plane has 360 total seats, which are divided into economy class and business class. For every 13 seats in economy class, there a
    10·1 answer
  • Use the Pythagorean theorem to find y.
    13·1 answer
  • 6th grade,PLSSSS HELP ME PLSSS, it’s on the imagee
    15·1 answer
  • Find h, k and a, then write an equation for the following transformed function.
    6·1 answer
  • 7)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!