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
user100 [1]
3 years ago
9

Given: MPNA pyramid All edges congruent AO = 36, AO ⊥ (MNP) Find: m∠AMO, AΔANM

Mathematics
1 answer:
Iteru [2.4K]3 years ago
6 0

Answer:

m∠AMO ≈ 54.7°

AΔANM = 486√3

Step-by-step explanation:

The edges are congruent, so all four faces are congruent equilateral triangles.  We'll say the length of each edge is 2r.

The height of the pyramid h is given to be 36.

The perpendicular distance from O to line MP is called the apothem (a).  Using 30-60-90 triangles, b = 2a and r = a√3.

Use cosine to find m∠AMO.

cos(∠AMO) = b / (2r)

cos(∠AMO) = (2a) / (2a√3)

cos(∠AMO) = 1 / √3

m∠AMO ≈ 54.7°

Use Pythagorean theorem to find the apothem.

(2r)² = b² + h²

(2a√3)² = (2a)² + 36²

12a² = 4a² + 1296

8a² = 1296

a² = 162

a = 9√2

So the edge length is:

2r = 2√3 (9√2)

2r = 18√6

The area of the equilateral triangle ΔANM is half the apothem times the perimeter:

A = ½aP

A = ½ (9√2) (3 × 18√6)

A = 243√12

A = 486√3

You might be interested in
What is the radius of a circle whose equation is x2 + (y – 8)2 = 25?
Dafna11 [192]
Use photo math :) and you will get your answer
8 0
3 years ago
Read 2 more answers
Harry and John share £60 in the ratio of 2: 1 work out how much money Harry gets ​
krek1111 [17]

Answer:

40

Step-by-step explanation:

3u-> 60

1u-> 20

2u->40

6 0
3 years ago
What is 9/4 minus 4/3
ahrayia [7]

Answer:

Step-by-step explanation:27/12 - 16/12 = 11/12

4 0
3 years ago
Read 2 more answers
A local hamburger shop sold a combined total of 522 hamburgers and cheeseburgers on Friday. There were 72 more cheeseburgers sol
max2010maxim [7]

Answer:

225 burgers

Step-by-step explanation:

522-72=450

450/2=225

5 0
3 years ago
adrian began riding his scooter at 7:00am. He stopped riding it at 8:10am. How long did adrian ride his scooter for?​
Alenkinab [10]

Answer:

Adrian rode his scooter for a total of 70 minutes, or an hour and ten minutes.

Step-by-step explanation:

There are 60 minutes in an hour, so if Adrian started riding his scooter at 7:00AM, to get to 8:10AM he needs to add 70.  Again, since there are 60 minutes in an hour, 70 minutes converts to one hour and 10 minutes.  Adrian rode his scooter for 70 minutes, or an hour and ten minutes.

7:00 + :70 = 8:10

8 0
3 years ago
Other questions:
  • Janelle types at the rate 3/8 of a page per minute. Which statement about janelle is true?
    9·1 answer
  • A seven-digit phone number in the united states consists of a three-digit exchange followed by a four-digit number.
    10·1 answer
  • 8 less than the product produc of 5 and -4
    8·2 answers
  • Explain in your own words how you would graph the equation y = -4x + 25
    11·1 answer
  • Tessa bought stock in a restaurant for $126.00. Her stock is now worth $163.80. What is the percentage increase of the value of
    11·1 answer
  • 100 POINTS HELP ME PLEASE!!!!! WILL MARK YOU BRAINIEST!!!!!!
    9·2 answers
  • What is the sum of all of the perfect squares between
    5·1 answer
  • Here is a list of numbers
    6·1 answer
  • Please help asap tysm <3
    14·1 answer
  • Simplify (x + y)² - (x - y)² + 2xy - 3x²​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!