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
Nitella [24]
3 years ago
7

What is the height of the triangle? A) 17 units B) 34units C) 51units D) 68units Help??

Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

51 units

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

The reason this is relevant here is that in your case, you start with an equilateral triangle, FGH. An equilateral triangle is also equiangular, so all angles are congruent and measure 60 deg.

m<F = m<FGH = m<H = 60 deg

When the height GR is drawn, <FGH is bisected creating two 30-60-90 degree triangles, FGR and HGR.

The altitude GR also bisects side HF, so

HR = FR = (1/2)HF = 17*sqrt(3)

In 30-60-90 degree triangle FRG, the short leg is FR; the long leg is GR; the hypotenuse is FG.

Now we use the ratio of the lengths of the sides of a 30-60-90 degree triangle.

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

We use only the short leg and long leg parts of the ratios.

17*sqrt(3) : GR = 1 : sqrt(3)

GR * 1 = 17 * sqrt(3) * sqrt(3)

GR = 17 * 3

GR = 51

You might be interested in
Please I need help with these 3 questions with explanation. See attached below.
amm1812

Answer:

  18. compound interest

  19. simple interest

  20. simple interest

Step-by-step explanation:

For these problems, the initial balance is irrelevant. All that matters is the multiplier of that balance. For simple interest at rate r for t years, the multiplier is ...

  simple interest multiplier = (1 +rt)

For interest compounded annually, the multiplier of the initial balance is ...

  compound interest multiplier = (1 +r)^t

A spreadsheet can do the computations for you.

___

As an example of the computations involved, consider problem 19:

  simple interest multiplier = 1 + 0.13·6 = 1.78

  compound interest multiplier = 1.10^6 = 1.771561

The latter is less than the former, so the simple interest account will have the (slightly) greater balance at the end of 6 years.

7 0
3 years ago
Your brother is 1/3 your age. Your sister is 6 years older than your bother. Your sister is 10. Write and solve an equation to f
maksim [4K]
A would be 12. If your sister is 6 years older than your brother your brother is 4

if your brother is 1/3 your age 4 times 3 you are 12
3 0
3 years ago
Read 2 more answers
Simplify (7^5)^3<br> A.7^8<br> B.(1/7)^15<br> C.35^3<br> D.7^15
oksano4ka [1.4K]

Answer:

\red{{7}^{15} }

Step-by-step explanation:

We know that,

{x}^{a}  \times  {x}^{b}  =  {x}^{a + b}  \\ ( {x}^{a} ) ^{b}  =  {x}^{ab}

Accordingly,

( {7}^{5} ) ^{3}  \\  {7}^{5 \times 3}  \\  {7}^{15}

8 0
2 years ago
Solve for b. 3(b−4)+5b=44 Enter your answer in the box.
I am Lyosha [343]

3b - 12 + 5b = 44

8b = 56

b = 7 (answer)

6 0
3 years ago
Read 2 more answers
Jenn recorded the favorite school subject of students at her school. she surveyed 700 students. how many more students chose Eng
sergij07 [2.7K]
105 students chose English than science
5 0
3 years ago
Read 2 more answers
Other questions:
  • Any suggestions for a word problem for the equation : 5/12 * 1/6?
    12·1 answer
  • Solve the equation 8x-12=5+15
    14·2 answers
  • How is a rational number that is not an integer different from a rational number that is an integer?
    6·1 answer
  • How to solve 8 to the power of five thirds
    14·1 answer
  • Find the area of the shape shown below
    8·1 answer
  • The polynomial x^3+8 is equal to
    9·2 answers
  • Consider the curve x+xy+2y^2=6. the slope of the line tangent to the curve at the point (2,1) is?
    11·2 answers
  • Question 10 (4 points) Point A, located at (4, 1), is reflected over the x-axis and then translated (x - 3, y + 7). Write the lo
    11·1 answer
  • The circumference C of a circle is found with the formula C=2(3.415)r​
    5·2 answers
  • PLSS HELP ASAPPP PLS What would be the sinuosity of this river:
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!