I need help on how to do this, picture attached. Thank you.

Mathematics

1 answer:

Lapatulllka [165]3 years ago

8 0

<h3>Answer:</h3>

ΔFDE ~ ΔFSR by the SSS similarity theorem

<h3>Step-by-step explanation:</h3>

Corresponding sides have the same ratios:

... FD/FS = 88/32 = 11/4

... DE/SR = 121/44 = 11/4

... EF/RF = 143/52 = 11/4

So, the triangles are similar by the SSS similarity theorem.

You might be interested in

What is the length of AC

meriva

Hi!
This is a fun one, as it delves into basic trigonometry.

We're going to use the Pythagorean theorem here, which says that for right triangles where "c" is the hypotenuse,

a² + b² = c²

We have to split this large triangle into two parts, both of which are right triangles. (This is why they drew a line in the middle to tell you that the larger triangle is composed of two right triangles.)

Let's do the one on the right first.

We know that the length of the hypotenuse is 10, and that the length of one of the legs is 6.5. If we plug this into our equation, we'll get the length of the other leg. I'm choosing "b" to be 6.5, but it really doesn't matter if you pick "a" or "b", so long as you reserve "c" for the hypotenuse (longest side).

a² + 6.5² = 10²
a² + 42.25 = 100
a² = 57.75
√a² = √57.75
a ≈ 7.6

Therefore, the length of DC is about 7.6.

Find the length of AD using the same method (7.5 is the hypotenuse "c", and 6.5 is one of the legs "a" or "b"). Then, once you have AD, add the lengths of AD and DC to get AC.

Have a great one!

7 0

3 years ago

Please help me with this

Len [333]

Answer:

60 degrees

Step-by-step explanation:

To first solve this problem, we need to figure out the size of an interior angle for a regular hexagon.

This can be done with the formula :

$angle = \frac{(n-2)*180}{n}$ , with n being the number of sides

A hexagon has 6 sides so here is how we would solve for the interior angle:

$\frac{(6-2)*180}{6}=120$ , with n= 6 sides

Now that we know that each interior angle in the hexagon is 120 degrees, we can now turn our attention to the rhombus.

The opposite angles of the rhombus are congruent, so the two larger obtuse angles are congruent, and so are the two smaller acute angles.

It is also important to note that a rhombus is a quadrilateral, so all of its interior angles add up to 360 degrees.

Looking at the rhombus, we already know one of the angles because it is shared by the interior angle of the hexagon, so the two larger angles in the rhombus are both 120 degrees.

But what about the smaller angles? All we need to do is subtract the two larger angles form 360 and divide by 2 to find the angle.

$\frac{360-2(120)}{2} = 60$ , so the smaller angle in the rhombus is 60 degrees.