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
irina [24]
3 years ago
15

A boat is 60m from the base of a lighthouse. The angle of depression between the lighthouse and the boat is 37°. How tall is the

lighthouse.

Mathematics
1 answer:
LekaFEV [45]3 years ago
6 0

Answer: 34.64 m

Step-by-step explanation:

Given: A boat is 60 m from the base of a lighthouse.

The angle of depression between the lighthouse and the boat is 37°.

By using trigonometric ratios :

\tan x=\dfrac{\text{Side opposite to }x}{\text{Side adjacent to }x}

here x= 37°, side opposite to x = height of lighthouse (h) , side adjacent to x = 60 m

\tan 37^{\circ}=\dfrac{h}{60}\\\\\Rightarrow\ 0.57735=\dfrac{h}{60}\\\\\Rightarrow\ h= 60\times0.57735\approx34.64

Hence, the lighthouse is 34.64 m tall.

You might be interested in
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng
chubhunter [2.5K]

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3\sqrt3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3\sqrt3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3\sqrt3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3\sqrt3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48\sqrt3]

Divide both sides by 0.04

275 = 24l + 48\sqrt3

Subtract 48\sqrt3 from both sides

24l = 275 - 48\sqrt3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

brainly.com/question/6613758

6 0
2 years ago
A player of the National Basketball Association’s Portland Trail Blazers is the best free-throw shooter on the team, making 94%
g100num [7]

Answer:

The data for the probabilities are shown in the table below.

- A represents the probability of making the two shots for each of the best and worst shooter on the Portland Trail Blazers' team

- B represents the probability of making at least one shot for each of the best and worst shooter on the Portland Trail Blazers' team.

- C represents the probability of not making any of the two shots for each of the best and worst shooter on the Portland Trail Blazers' team.

N | Best ||| Worst

A | 0.8836 | 0.3136

B | 0.9964 | 0.8064

C | 0.0036 | 0.1936

It becomes evident why fouling the worst shooter on the team is a better tactic. The probabilities of the best shooter making the basket over the range of those two free shots are way better than the chances for the worst shooter.

Step-by-step explanation:

Part 1

Probability of the best shooter of the National Basketball Association’s Portland Trail Blazers making a shot = P(B) = 94% = 0.94

Probability that he doesn't make a shot = P(B') = 1 - 0.94 = 0.06

a) Probability that the best shooter on the team makes the two shots awarded = P(B) × P(B) = 0.94 × 0.94 = 0.8836

b) Probability that the best shooter on the team makes at least one shot.

This is a sum of probabilities that he makes only one shot and that he makes two shots.

Probability that he makes only one shot

= P(B) × P(B') + P(B') + P(B)

= (0.94 × 0.06) + (0.06 × 0.94) = 0.1128

Probability that he makes two shots = 0.8836 (already calculated in part a)

Probability that he makes at least one shot = 0.1128 + 0.8836 = 0.9964

c) Probability that the best shooter on the team makes none of the two shots = P(B') × P(B') = 0.06 × 0.06 = 0.0036

d) If the worst shooter on the team, whose success rate is 56% is now fouled to take the two shots.

Probability of the worst shooter on the team making a shot = P(W) = 56% = 0.56

Probability that the worst shooter on the team misses a shot = P(W') = 1 - 0.56 = 0.44

Part 2

a) Probability that the worst shooter on the team makes the two shots = P(W) × P(W)

= 0.56 × 0.56 = 0.3136

b) Probability that the worst shooter on the team makes at least one shot.

This is a sum of probabilities that he makes only one shot and that he makes two shots.

Probability that he makes only one shot

= P(W) × P(W') + P(W') + P(W)

= (0.56 × 0.44) + (0.44 × 0.56) = 0.4928

Probability that he makes two shots = 0.3136 (already calculated in part a)

Probability that he makes at least one shot = 0.4928 + 0.3136 = 0.8064

c) Probability that the worst shooter makes none of the two shots = P(W') × P(W') = 0.06 × 0.06 = 0.1936

From the probabilities obtained

N | Best ||| Worst

A | 0.8836 | 0.3136

B | 0.9964 | 0.8064

C | 0.0036 | 0.1936

It becomes evident why fouling the worst shooter on the team is a better tactic. The probabilities of the best shooter making the basket over the range of those two free shots are way better than the chances for the worst shooter.

Hope this Helps!!!

8 0
3 years ago
Read 2 more answers
If Steve's age is decreased by 12 years, and that difference is multiplied by 3, the result is 24 years. Find Steve's age.
kumpel [21]

Answer:

20 years old.

Step-by-step explanation:

Go backwards in the equation.

24/3 = 8

8+12

= 20

8 0
3 years ago
HELPPPP PLEASSEEEEE Literal Equations and Formulas
Lapatulllka [165]

Answer:

Im pretty sure A

Step-by-step explanation:

multiply both sides by 3/4 (reciprocal)

3/4X=pie(r)cubed

divide by pi on both sides

3/4X

-------- = r(cubed)

pi

cube root both sides

4 0
3 years ago
PLZ ANSWER ILL GIVE BRAINILEST2 box plots. The number line goes from 26 to 36. For Pleasantville Middle School, the whiskers ran
Svetach [21]

Answer:

I believe the answer is- The mean and MAD can accurately describe the "typical" value in the symmetric data set.

Step-by-step explanation:

The other answers don't make sense because the mean and MAD are being used for symmetrical distributions and asymmetrical means uneven distributions.

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is 32 plus 60 divided by 135 ?
    6·2 answers
  • What is her change in elevation after 5 Hours
    15·1 answer
  • Find the length of the arc intercepted by an angle of 36° in a circle with radius 12 inches
    14·1 answer
  • How do i use distributive property to rewrite 4x (25 + 4)???
    7·2 answers
  • What is the value of the expression below when z = 6
    6·1 answer
  • In a 30-60-90 right triangle, the side opposite the 30- degree angle is?
    9·2 answers
  • In the accompanying diagram, EF intersects AB and CD at G and H, respectively, and GI is drawn such
    6·1 answer
  • Rearrange the formula for V = lwh to solve for l.
    7·1 answer
  • J3.
    6·1 answer
  • What is the name for a mathematical phrase? O A. An inequality OB. An operation OC. An expression OD. An equation​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!