PLEASE HELP!!! What is the value of x? Enter your answer in the box. x =

In angle def , DF=22 and m angle f=45. Find the length of a leg. Leave your answer in simplest radical form

Levart [38]

The figure is the right triangle DEF.

In it, E is the 90° angle, D is the corner over E (this is, DE is the vertical segment or height from the base) and F is the corner to the right of E (f, is the angle and EF is the horizontal segment or base of the triangle).

Then EF is the adjacent leg to the angle f, DE is the opposite leg to the angle f, and DF is the hypotenuse of the triangle.

Given that the angle f is 45°, you know that the triangle is isosceles (45-45-90) and then the two legs have the same length and you can use Pytagorean theorem:

DF^2 = x^2 + x^2 = 2x^2 => x^2 = (DF)^2 / 2

Taking square roots from both sides:

=> x = DF / √2 = 22 / √2 = [22√2] / [(√2)(√2)] = [22√2] / 2 = 11√2

Remember, both legs have the same length.

Answer: 11√2

6 0

3 years ago

In the figure below, AB=AE, AC=AD and AP is perpendicular to BE. Prove that BC=DE.

NISA [10]

Step-by-step explanation:

1) In the figure, as AB is equal to AE, ABE is an equilateral triangle.

As AP is perpendicular to BE

=> AP is the height of the triangle ABE.

In an equilateral triangle, the median and the height is the same, so that AP is also the median of the triangle.

=> P is the midpoint of BE

=> PE = PB

2) In the figure, as AC = AD, so that ACD is an equilateral triangle.

As AP is perpendicular to BE, so that it is perpendicular to CD as well

=> AP is the height of the triangle ACD

In an equilateral triangle, the median and the height is the same, so that AP is also the median of the triangle ACD.

=> P is the midpoint of CD

=> PC = PD

We have:

+) PB = PE

+) PC = PD

=> PB - PC = PE - PD => BC = DE

5 0

4 years ago

ACBM is a segment of a circle such

tatiyna

Answer:

a. 8.94 cm b. 127° c. 12.37 cm²

Step-by-step explanation:

a. Since CM = 4 cm is the perpendicular bisector of AB = 16 cm and r is the radius off the circle. From Pythagoras' theorem,

r² = (AB/2)² + CM²

r = √[(AB/2)² + CM²]

Substituting the values of the variables into r, we have

r = √[(16/2)² + 4²]

r = √[8² + 4²]

r = 4√[2² + 1²]

r = 4√[4 + 1]

r = 4√5 cm

r = 8.94 cm

b. We know that the length of a chord L = 2rsin(θ/2) where r is the radius of the circle, and θ is the angle subtended by the chord AB.

Since L = 2rsin(θ/2) and L = AB = 16 cm,

L/2r = sin(θ/2)

taking sine inverse of both sides, we have

θ/2 = sin⁻¹(L/2r)

multiplying both sides by 2, we have

θ = 2sin⁻¹(L/2r)

substituting the values of the variables, we have

θ = 2sin⁻¹[16/(2 × 8.94)]

θ = 2sin⁻¹[16/17.88]

θ = 2sin⁻¹[0.8949]

θ = 2 × 63.49°

θ = 126.98°

θ ≅ 127°

c. The area of a segment A is given by

A = (θπ/360 - sinθ)r²/2 where θ is the angle subtended by the segment and r = radius of the circle

since θ ≅ 127° and r = 4√5 cm, substituting these values into A, we have

A = (127°π/360 - sin127°)(4√5)²/2

A = (398.93/360 - 0.7988)40

A = (1.1081 - 0.7988)40

A = 0.3093 × 40

A = 12.372 cm²

A ≅ 12.37 cm²

5 0

3 years ago

What is the solution for -10 -19 A.)x > -19 B.)x -1

Ira Lisetskai [31]

Answer:A

Step-by-step explanation:positive is bigger then negative.

3 0

3 years ago

Read 2 more answers

Geometry page 1 help please !

victus00 [196]

Answer:

16) $y=\frac{1}{4}x +5$

17) y = -x - 4

18) y = -2x - 1

19) y = -2x

20) $y=\frac{-5}{3} -3$

Step-by-step explanation:

With the two points you find the slope using $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

Then using that slope, plug the slope in with one of the points values of x and y into the point slope formula, and smiplify that into the y-intercept formula.

6 0

3 years ago