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
Slav-nsk [51]
3 years ago
14

A rhombus ABCD has AB = 10 and m∠A = 60°. Find the lengths of the diagonals of ABCD.

Mathematics
1 answer:
melisa1 [442]3 years ago
8 0
Three important properties of the diagonals of a rhombus that we need for this problem are:
1. the diagonals of a rhombus bisect each other
2. the diagonals form two perpendicular lines
3. the diagonals bisect the angles of the rhombus

First, we can let O be the point where the two diagonals intersect (as shown in the attached image). Using the properties listed above, we can conclude that ∠AOB is equal to 90° and ∠BAO = 60/2 = 30°. 

Since a triangle's interior angles have a sum of 180°, then we have ∠ABO = 180 - 90 - 30 = 60°. This shows that the ΔAOB is a 30-60-90 triangle.

For a 30-60-90 triangle, the ratio of the sides facing the corresponding anges is 1:√3:2. So, since we know that AB = 10, we can compute for the rest of the sides.

\overline{OB}:\overline{AB} = 1:2
\overline {OB}:10 = 1:2
\overline{OB} = \frac{1}{2}(10) = 5

Similarly, we have

\overline{AO}:\overline{AB} = \sqrt{3}:2
\overline {AO}:10 = \sqrt{3}:2
\overline{AO} = \frac{\sqrt{3}}{2}(10) = 5\sqrt{3}

Now, to find the lengths of the diagonals, 

\overline{AD} = 2(\overline{AO}) = 10\sqrt{3}
\overline{BC} = 2(\overline{OB}) = 10

So, the lengths of the diagonals are 10 and 10√3.

Answer: 10 and 10√3 units

You might be interested in
Joanne cannot decide which of two washing machines to buy. The selling price of each is ​$480 The first is marked down by ​%50 T
serious [3.7K]

Answer:

i can not be cas  thae are the same

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Can someone please help me with this ?
serg [7]

Answer:

Area = 25 cm²

Diagonal = 10.6cm

8 0
3 years ago
Help!!!!!!!!!!!! !!!!!!!!!!!!
yulyashka [42]
The correct answer is y=2/3x+4 which is the last option :)
6 0
3 years ago
Read 2 more answers
What percent is the change in the price if the price was $100 and now it is $1250?
Vsevolod [243]

Answer:

  1150%

Step-by-step explanation:

The percentage change is ...

  percentage change = (amount of change)/(original amount) × 100%

  = ((new amount) - (original amount))/(original amount) × 100%

  = ($1250 -$100)/$100 × 100%

  = 1150/100 × 100%

  = 1150%

6 0
3 years ago
Read 2 more answers
Ratio of boys to girls is 3 to 4, the team has 70 members. How many are boys.
elena-14-01-66 [18.8K]
There is 30 boys
 and 40 girls
5 0
2 years ago
Read 2 more answers
Other questions:
  • Timothy bought 10 cookies for $5.00. Let x represent the number of cookies purchased, and let y represent the total cost. Graph
    6·2 answers
  • Between 1-50 what number are composite?
    7·1 answer
  • Can someone please solve #8
    6·1 answer
  • 41.2 x 1.5. Then explain where the decimal point should go and why
    14·2 answers
  • Convert 10 meters to feet (round to the nearest tenth)
    13·1 answer
  • A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27nft3. Which equation gives the volume o
    8·2 answers
  • WHO WANTS FREE BRAINLY AND TEN POINTS???
    10·2 answers
  • If there are 21 students in class today how much would it cost for the class and your teacher to ride the sandia aerial tram? ra
    13·1 answer
  • El número 9 es un número primo?
    6·1 answer
  • 1. Jill bikes 15 miles in the morning and 17 miles in the afternoon. How many miles does she bike in all? Equation: miles 7 | Le
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!