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
aliina [53]
3 years ago
10

Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who

is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack's and John's eyes are 1.5 meters from the ground and the distance from Jack's eyes to the top of the tower is 50.64 meters, how far is John from the base of the tower? Round your answer to the nearest tenth.
A.
24.5 meters

B.
16.1 meters

C.
22.2 meters

D.
18.8 meters

Mathematics
1 answer:
zmey [24]3 years ago
8 0

Answer:

18.7939 m

Step-by-step explanation:

-Let x be the distance between John and clock tower.

-Let y be the vertical distance from the eyes of the two men  standing to the top of the clock tower.

#Taking the right triangle ACD:

\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5

#Taking the right triangle ABD:

\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5

#We equate the two yo solve for x and y;

(x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939

Hence, John's distance from the tower's base is 18.7939 m

You might be interested in
If 8(a + b) = 48, what is the value of a + b?
Cloud [144]

Answer:

8(a + b) = 48 \\  \\ a + b =  \frac{48}{8}  \\  \\ a + b = 6

I hope I helped you^_^

5 0
3 years ago
Write an expression for the area of this sweetuare
nata0808 [166]
Length = x + y

Area of a square = Length x Length

The expression can be :

1)  Area of the square = (x + y)(x + y) 

2) Area of the square = (x + y)²

3) Area of the square = x² + 2xy + y²
5 0
3 years ago
Are the two expressions equivalent 5(3x+8) 8x+8 when x=10
Brums [2.3K]

Answer:no

Step-by-step explanation:

5(3(10)+8)

5(30+8)

5(38)=190

8(10)+8

80+8

88

88≠190 so no

7 0
3 years ago
Read 2 more answers
Vic is standing on the ground at a point directly south of the base of the CN Tower and can see the top when looking at an angle
Sindrei [870]

The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

<h3>How can the distance between Vic and Dan be calculated?</h3>

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

tan( \theta) =  \frac{opposite}{adjacent}

tan( 61 ^{ \circ}) =  \frac{553.3}{ Vic' s\: distance \: to \: tower}

distance  =  \frac{553.3}{tan ( {61}^{ \circ} )}  = 306.7

  • Vic's distance from the tower ≈ 306.7 m

Similarly, we have;

Dan's distance  =  \frac{553.3}{tan ( {72}^{ \circ} )}  = 179.8

  • Dan's distance from the tower ≈ 179.8 m

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan <em>d </em>is found as follows;

  • d = √(306.7² + 179.8²) ≈ 356

Therefore;

  • Vic is approximately 356 meters from Dan

Learn more about Pythagorean theorem here:

brainly.com/question/343682

#SPJ1

4 0
2 years ago
It takes la’mya 4 hours to knit 2 yards of a blanket . How many yards can she knit in one hour ?
shtirl [24]

Answer:

she can knit 1/2 a yard of a blanket in 1 hour.

So it would look like this

1/2 a yard of blanket

-----

1 hour

It would be, she can knit one half of a yard of blanket in one hour

one half over oner hour

6 0
3 years ago
Other questions:
  • ANYONE PLEASE HELP. BEST ANSWER GETS BRAINLIEST
    12·2 answers
  • Which statement is true about the equation (x – 4)(x + 2) = 16? The equation x – 4 = 16 can be used to solve for a solution of t
    8·2 answers
  • P is a point on CD. If CP : PD is 7 : 2 and CD is 54, what are the lengths of CP and PD?
    13·1 answer
  • An object with a mass of 2000 g accelerates 8.3 m/s² when an unknown force is applied to it. What is the amount of force?
    15·1 answer
  • Jo participated in a read-a-thon to raise money for a local library. She raised $20 plus $1.50 per book that she red. She raised
    10·1 answer
  • A woman exerts a horizontal force of 10 pounds on a box as she pushes it up a ramp that is 8 feet long and inclined at an angle
    12·1 answer
  • Identify the slope and y-intercept for each linear function's equation.
    8·1 answer
  • Find the Volume of the box using the Pythagorean Theorem.
    9·2 answers
  • A book contains the following recommend weight for kangaroos:" Give the kangaroo 120 pounds for the first 5 feet plus 5 pounds f
    13·1 answer
  • Una empreza tiene contratadas 75 personas. En las oficinas trabaja el 16% de los hombres y 20% de mujeres, si el total de person
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!