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
Nezavi [6.7K]
3 years ago
7

The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base and PA = 2sqrt5 in. The base edges AB = 10 in, AC

= 17 in, and BC = 21in. Find the length of the segment PQ if Q ∈ BC and AQ is the altitude of the base.
Mathematics
1 answer:
DIA [1.3K]3 years ago
6 0

Answer:

PQ = √84 = 2√21 in ≈ 9.165 in

Step-by-step explanation:

The base edges AB = 10 in, AC = 17 in, and BC = 21 in

Q ∈ BC and AQ is the altitude of the base.

Let BQ = x in ⇒ CQ = (21 - x) in

ΔAQB a right triangle at Q

∴ AQ² = AB² - BQ² = 10² - x²  ⇒(1)

ΔAQC a right triangle at Q

∴ AQ² = AC² - CQ² = 17² - (21-x)²  ⇒(2)

Equating (1) and (2)

∴  10² - x² = 17² - (21-x)²

∴ 10² - x² = 17² - (21² - 42x + x²)

∴  10² - x² = 17² - 21² + 42x - x²

∴ 10² - 17² + 21² = 42x

∴ 42x = 252

∴ x = 252/42 = 6

Substitute at (1)

∴ AQ² = AB² - BQ² = 10² - x² = 100 - 36 = 64 = 8²

∴ AQ = 8 in

∵ The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base

∴ PA⊥AQ

∴ ΔPAQ is a right triangle at A,

PA = 2sqrt5 in  and AQ = 8 in

∴ PQ (hypotenuse) = √(PA² + AQ²)

∴ PQ = √[(2√5)² + 8²] = √(20+64) = √84 = 2√21 in ≈ 9.165 in

You might be interested in
Is the number 4.333..... rational or irrational?
AleksAgata [21]

Answer:

Irrational number

7 0
3 years ago
Find the probability of rolling a 5 or greater on the first die and a 2 or greater on the second die
bekas [8.4K]

Answer:

The probability is 1/9

Step-by-step explanation:

The probability of rolling a 5 the first time is 1/6

The probability of rolling a number greater than 2

Numbers greater than 2 are 3, 4, 5, 6

So the probability of rolling a number out of these four is 4/6

So the probability of rolling a five for the first time and the probability of rolling a number greater than 2 the second time will be

1/6 * 4/6 = 4/36 = 1/9

6 0
3 years ago
Read 2 more answers
The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data ar
laiz [17]

Answer:

Step-by-step explanation:

5 0
3 years ago
Which set of side lengths form a right triangle?
vova2212 [387]

Answer:

 Answer is 7cm,8cm,10cm

Step-by-step explanation:

A^2+B^2=C^2

6 0
3 years ago
Read 2 more answers
When angles are complementary, the sum of their measures is 90 degrees.Two complementary angles have measures of 2x-10 degrees a
Mariana [72]

Complementary angles are those angles whose sum is 90 degree.

The measurement of two complementary angles are

(2x-10), (3x-10)

There sum have to be 90 degree. That is

2x-10+3x-10 = 90

Combining like terms ,

5x - 20 = 90

Moving 20 to right side

5x=110

Dividing both sides by 5

x =22

So the measurement of the angles are

2*22-10 , 3*22-10  \\
34 degree,  56 degree

6 0
3 years ago
Other questions:
  • 7b-2/5=6b-7/5 <br> solve for b
    13·2 answers
  • What is the meaning for “mean” in math?
    10·2 answers
  • CD is the perpendicular bisector of both XY and ST, and CY=20. Find SX.
    14·2 answers
  • Sqrt(3x)-1=-4<br><br> 1.)x=3<br><br> 2.)x=-3<br><br> 3.) no solution<br><br> 4.)x= 25/3
    7·1 answer
  • Ronna answered 18 of the 20 questions on her second math test correctly. On the first test, she had answered only 15 of 20 quest
    7·1 answer
  • Rounded to the nearest tenth, what is the area of rectangle ABDC?
    14·1 answer
  • An explanation would be great. thank you​
    13·1 answer
  • Will give brainliest! |^^^|
    14·2 answers
  • The circle graph shows the results of a survey of registered voters the day of an election Which Party's Candidate Will Get Your
    14·1 answer
  • A school is arranging a field trip to the zoo. The school spends 635.66 dollars on passes for 34 students and 3 teachers. The sc
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!