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2 years ago

What is the length of EF in the right triangle below?

Mathematics

2 answers:

Lyrx [107]2 years ago

8 0

Answer:

\sqrt(217)

Step-by-step explanation:

(19)^2=(12)^2

361 - 144 + 217

\sqrt(217)

andriy [413]2 years ago

8 0

Answer:

$\sqrt{217}units$

Step-by-step explanation:

Given : A right angled triangle EFD

Hypotenuse = ED=19 units

Base = DF =12 units

Perpendicular = EF

Solution:

To find length of EF we will use Pythagorean Theorem:

$(Hypotenuse)^{2}=(Perpendicular)^{2}+(Base)^{2}$

$ED^{2}=EF^{2}+DF^{2}$

$19^{2}=EF^{2}+12^{2}$

$361=EF^{2}+144$

$361-144=EF^{2}$

$217=EF^{2}$

$\sqrt{217} =EF$

Thus the length of EF is $\sqrt{217}units$

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In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.