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
guapka [62]
3 years ago
11

A boat is sighted from a 50-meter observation tower on the shoreline at an angle of depression of 4 degrees moving directly towa

rds the shore at a constant speed. Five minutes later the angle of depression of the boat is 12 degrees. What is the speed of the boat in kilometers per hour?
Mathematics
1 answer:
MAXImum [283]3 years ago
4 0

Answer:

  5.76 km/h

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).

  Tan = Opposite/Adjacent

  tan(4°) = (height of tower)/(distance from shore)

  tan(4°) = (50 m)/(distance from shore)

Then the distance from shore is ...

  distance from shore = (50 m)/tan(4°) ≈ 715.03 m

__

At the second sighting, the distance from shore is ...

  distance from shore = (50 m)/tan(12°) ≈ 235.23 m

So, the distance traveled in 1/12 hour is ...

  715.03 m - 235.23 m = 479.80 m

and the speed in km per hour is ...

  speed = 0.4798 km/(1/12 h) = 5.7576 km/h

The speed of the boat is about 5.76 km per hour.

You might be interested in
Which is the best definition of the radius of a circle​
lapo4ka [179]

Answer:

The radius is half of the diameter of the circle and it is measured from the center of the circle to the circumference of the circle.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Triangle ABC is an isosceles with a base AC. The base angles are 60 degrees. Find the length of the base and the length of the a
lisabon 2012 [21]

Answer:

base =5   because all angles=60, so an equilateral triangle

height=4.33

Step-by-step explanation:

height^2+1/2(5)^2=5^2

height^2+6.25=25

height^2=18.75

height=4.33

8 0
2 years ago
HELPP 35 POINTS!!!!! Point Q is the center of Circle Q in the diagram below. The measure of angle XAY is 72° (m∠XAY = 72°). Sinc
Paladinen [302]

Answer:

Se explanation

Step-by-step explanation:

The diagram shows the circle with center Q. In this circle, angle XAY is inscribed angle subtended on the arc XY. Angle XQY is the central angle subtended on the same arc XY.

The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle. Therefore,

m\angle XBY=2m\angle XAY=2\cdot 72^{\circ}=144^{\circ}

The measure of the intercepted arc XY is the measure of the central angle XQY and is equal to 144°.

All angles that have the same endpoints X and Y and vertex lying in the middle of the quadrilateral XAYQ have measures satisfying the condition

72^{\circ}

because angle XAY is the smallest possible angle subtended on the arc XY in the circle and angle XQY is the largest possible angle in the circle subtended on the arc XY.

6 0
3 years ago
Find the midpoint of the line segment whose endpoints are (2.6,5.1) and (3,4.7).
svp [43]

Answer:

Mid point is: (2.8;4.9)

Step-by-step explanation:

To find midpoint of a line segment we can use the general equation:

Mid=\frac{x_1+x_2}{2} ;\frac{y_1+y_2}{2}

Where the point of the line are: (x₁;y₁) and (x₂;y₂).

In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:

Mid=\frac{2.6+3}{2} ;\frac{5.1+4.7}{2}

<h3>Mid point is: (2.8;4.9)</h3>

7 0
3 years ago
PLEASE HURRY!!! Combine like terms to simplify the expression: 1.17-0.07a+(-3.92a) Thanks and have a great day! :)
Alex_Xolod [135]

Answer:

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Find the zeros of each function. State the multiplicity of any multiple zeros. (Please show work)
    13·1 answer
  • I need help with this math question
    12·1 answer
  • Help please come asp
    13·1 answer
  • When she graduates college Linda will owe 43,000 in student loans. The interest rate on the federal Liana is 4.5 % and the rate
    10·1 answer
  • Order the values from least to greatest. -21/2 -1/2, |1/2|, 1 1/2, |-2|, |-2 1/2|​
    12·1 answer
  • 3x + y = – 7<br> Solve to find were the two point intercept
    9·1 answer
  • Please answer as soon as possible. Use the graphing tool to graph this system of equations.​
    11·1 answer
  • 5x-3(x-2)=4 <br><br> This is for Algebra 1
    12·1 answer
  • El interior de un tanque que contiene agua, tiene una presión manométrica de 300 kPa. ¿Qué profundidad tiene el tanque de agua?
    12·1 answer
  • Let a=3/5 and let b=2/3. Compute a^2b^-3.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!