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3 years ago

For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH.

Mathematics

1 answer:

Whitepunk [10]3 years ago

5 0

Answer:

Option 4 : 19

Step-by-step explanation:

For trapezoid ABCD : AB = 16 and CD = 28

E and F are midpoints of the legs

So, EF = (AB + CD)/2 = (16+28)/2 = 44/2 = 22

GH be the median of ABFE

So, GH = (AB + EF)/2 = (16+22)/2 = 38/2 = 19

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Read 2 more answers

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

EastWind [94]

Answer:

The Law of Sines applies to any triangle and works as follows:

a/sinA = b/sinB = c/sinC

We are attempting to solve for every angle and every side of the triangle. With the given information, A = 61°, a = 17, b = 19, we can solve for the unknown angle that is B.

a/sinA = b/sinB

17/sin61 = 19/sinB

sinB = (19/17)(sin61)

sinB = 0.9774

sin-1(sinB) = sin-1(0.9774)

B = 77.8°

With angle B we can solve for angle C and then side c.

A + B + C = 180°

C = 180° - A - B

C = 180° - 61° - 77.8°

C = 41.2°

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17/sin61 = c/sin41.2

c = 17(sin41.2/sin61)

c = 12.8

The first solved triangle is:

A = 61°, a = 17, B = 77.8°, b = 19, C = 41.2°, c = 12.8

However, when we solved for angle B initially, that was not the only possible answer because of the fact that sinB = sin(180-B).

The other angle is simply 180°-77.8° = 102.2°. Therefore, angle B can also be 102.2° which will give us different values for c and C.

C = 180° - A - B

C = 180° - 61° - 102.2°

C = 16.8°

a/sinA = c/sinC

17/sin61 = c/sin16.8

c = 17(sin16.8/sin61)

c = 5.6

The complete second triangle has the following dimensions:

A = 61°, a = 17, B = 102.2°, b = 19, C = 16.8°, c = 5.6

The answer you are looking for is the first option given in the question:

B = 77.8°, C = 41.2°, c = 12.8; B = 102.2°, C = 16.8°, c = 5.6

Step-by-step explanation:

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3 years ago

The circumference of a circle is 12 inches. What is the radius

IceJOKER [234]

Greetings!

"The circumference of a circle is 12 inches. What is the radius?"...

We can use the formula to find the circumference of circle to solve this:
 $2 \pi r$

Input the information we know:
 $2 \pi r=12$

Solve for r, using the properties of equality:

Simplify.
 $6.28r=12$
Divide both sides by 6.28
 $(6.28r)/6.28=(12)/6.28$ 
Simplify.
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The radius is 1.91cm long.

Hope this helps.
-Benjamin

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3 years ago

For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH.​

For trapezoid ABCD, E and F are midpoints of the legs. Let GH be the median of ABFE. Find GH.