Hannah leans a 16-foot ladder against a wall so that it forms an angle of 61° with the
ground. What's the horizontal distance between the base of the ladder and the wall?
Round your answer to the nearest tenth of a foot if necessary.

Given:

In triangle ABC, [tex]m\angle A=66^\circ, AB=5\text{ mi}[/tex].

To find:

The angle of depression from point A to point C.

Solution:

According to angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]

[tex]66^\circ+90^\circ+m\angle C=180^\circ[/tex]

[tex]156^\circ+m\angle C=180^\circ[/tex]

[tex]m\angle C=180^\circ-156^\circ[/tex]

[tex]m\angle C=24^\circ[/tex]

We know that if a transversal line intersect the two parallel lines, then alternate interior angles are equal. So, the angle of depression from point A to point C is equal to the measure of angle C in triangle ABC.

Therefore, the angle of depression is 24 degrees.

9514 1404 393

Answer:

  46

Step-by-step explanation:

The length of base CD is twice the length of midsegment FG, so you can write the equation ...

  CD = 2×FG

  -3x +52 = 2(13 +5x)

  52 = 26 +13x . . . . . . . . add 3x, simplify

  26 = 13x . . . . . . . . . subtract 26

  2 = x . . . . . . . . . . divide by 13

Then the measure of CD is ...

  CD = -3x +52 = -3(2) +52 = -6 +52

  CD = 46

Answer:

46 miles

Step-by-step explanation:

First, find the distance traveled by the person riding at 20 mph.

Multiply 20 by 2:

20(2)

= 40 miles

Find the distance traveled by the person riding at 3 mph.

Multiply 3 by 2:

3(2)

= 6 miles

Add these distances together:

40 + 6

= 46

So, the total distance is 46 miles

Answer:

46 miles

Step-by-step explanation:

Assuming both travel at a constant rate of miles per hour.

Time allowed: 2 hours.

Biker: 20 miles/hr, or (20 x 2) miles/ (2 x 1) hrs. = 40 miles/ 2 hours

Walker: 3 miles/hr or (3 x 2) miles/(2 x 1) hrs. = 6 miles/2 hours.

You are finding the total distance traveled together, and so add the two miles together:

40 + 6 = 46

46 miles in 2 hours is your answer.

~

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

Given

[tex] \frac{ \sin(60) \sec(60) \cot(30) }{ \cos( 45) ) } [/tex]

Using the unit circle, we know that

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

[tex] \cos(45) = \frac{ \sqrt{2} }{2} [/tex]

We can find sec and cot by using reciprocal identies.

[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]

[tex] \cos(60) = \frac{1}{2} [/tex]

So

[tex] \sec(60) = 2[/tex]

[tex] cot(x) = \frac{1}{ \tan(x) } [/tex]

[tex] \tan(30) = \frac{1}{ \sqrt{3} } [/tex]

so

[tex] \cot(30) = \sqrt{3} [/tex]

Plug in the values.

[tex] \frac{ \frac{ \sqrt{3} }{2} \times 2 \times \sqrt{3} }{ \frac{ \sqrt{2} }{2} } [/tex]

[tex] \frac{ \frac{ \sqrt{3} }{2} \times \frac{ \sqrt{12} }{1} }{ \frac{ \sqrt{2} }{2} } [/tex]

[tex] \frac{3}{ \frac{ \sqrt{2} }{2} } [/tex]

[tex]3 \sqrt{2} [/tex]

Answer:

55

Step-by-step explanation:

The answer is 55 as distance is a scalar quantity that means quantities that depend on magnitude and not on direction. Therefore we cannot write - 55 as answer.

9514 1404 393

Answer:

  4) 95.7 m

Step-by-step explanation:

The angle at the cliff base between Alan and Keith is ...

  B = 180° -29° -48° = 103°

The law of sines will tell you the distance KB from Keith to the cliff base is

  KB/sin(A) = KA/sin(B)

  KB = KA×sin(A)/sin(B) = (70 m)sin(29°)/sin(103°) ≈ 34.82935 m

The height of the cliff is found from the tangent relation ...

  Tan = Opposite/Adjacent

  tan(70°) = height/(34.83 m)

  height = (34.83 m)tan(70°) = 95.693 m

The height of the cliff is about 95.7 m.

_____

Additional comment

These problems can usually be resolved into two 2-D problems. Here, we can work out the distance we need from Keith to the cliff by considering only the ground plan of the site. Then we can work out the height of the cliff only considering the vertical plane containing Keith and the base of the cliff.

The attachment shows the ground plan triangle KAB.

Answer:

56 degrees

Step-by-step explanation:

We know, the sum of the three angles of any triangle is equal to 180 degrees.

63 + 61 = 124

Now, 180 - 124 = 56 degrees

Hope this will help. Please give me brainliest.

Answer:

hey, there is no attached photo. so I don't know how to help

Answer:

40%

Step-by-step explanation:

Because you want to know the total percent the price increased so you add the amounts. 30% plus 10% makes 40%

Step-by-step explanation:

We need to find a midpoint. A midpoint splits the two end coordinates to meet at a point.

Use midpoint formula

[tex] \frac{ - 2 + 10}{2} = 4[/tex]

[tex] \frac{ - 11 + 1}{2} = - 5[/tex]

So the coordinates will be at

(4,-5)

Answer:

(11 x 8) x 5

Step-by-step explanation:

We find volumes of rectangular prims by multiplying the length by the width to get the area of a said prism, and multiplying the area by the height in order to get the volume.

Answer:

A

Step-by-step explanation:

Given:

The figure of a quadrilateral ABCD.

To find:

The perimeter of the quadrilateral ABCD.

Solution:

In an isosceles triangle, the two sides and base angles are congruent.

In triangle ABD,

[tex]\angle DAB\cong \angle ABD[/tex]               [Given]

[tex]\Delta ABD[/tex] is an isosceles triangle      [Base angle property]

[tex]AD=BD[/tex]                   [By definition of isosceles triangles]    

[tex]8=BD[/tex]                   ...(i)

In triangle BCD,

[tex]\angle BCD\cong \angle CDB\cong \angle CBD[/tex]        [Given]

All interior angles of the triangle BCD are congruent, so the triangle BCD is an equilateral triangle and all sides of the triangle area equal.

[tex]BC=CD=BD[/tex]

[tex]BC=CD=8[/tex]      [Using (i)]               ...(ii)

Now, the perimeter of quadrilateral ABCD is:

[tex]Perimeter=AB+BC+CD+AD[/tex]

[tex]Perimeter=11+8+8+8[/tex]

[tex]Perimeter=35[/tex]

Therefore, the perimeter of the quadrilateral ABCD is 35 units.

Answer:

cccccccccccccccccccc

Answer:

a) 10 salads

b) 5 Choose 2 and 5 Choose 3 result in the same amount

Step-by-step explanation:

a) ₅C₂ = 5! / (5-2)! 2!

= 5! / 3! 2!

= (5 × 4) / 2

= 10 salads

b) ₅C₃ = 5! / (5-3)! 3!

= 5! / 2! 3!

= (5 × 4) / 2

= 10

Answer:

245 cubic inches

Step-by-step explanation:

The volume of a rectangular prism is length times width times height.

So in this case we would do, 8 * 2.5 * 12.25 to get 245. So your answer would be 245 cubic inches.

*side note*: 2 1/2 is the same thing as 2.5 and 12 1/4 is the same thing as 12.25

Answer:

Step-by-step explanation:

same side interior angles also mean co interior angle

heree,

1.angle 4 and 6 are same side interior angle

2.angle 3 and 5 are also same side interior angle.

Co-interior angles or same side interior angles  lie between two lines and on the same side of a transversal. In each diagram the two marked angles are called co-interior angles. If the two lines are parallel, then co-interior angles add to give 180o and so are supplementary.

Step-by-step explanation:

i) Angle 4 and 6

ii) Angle 3 and 5

Answer:

x = -1

Step-by-step explanation:

8 = 2^(x + 4)

Rewriting 8 as 2^3

2^3 = 2^(x + 4)

Since the bases are the same, the exponents must be the same

3 = x+4

Subtract 4 from each side

3-4 =x+4-4

-1 =x

Answer:

This is the answer :

x=–1

Choose (B)

OPTION A

y= 3x+6

This equation satisfies for all the value given in the table.

For (0,6)

y = 3(0)+6 = 6

For (2,12)

y=3(2) +6 = 6+6= 12

And so on.

Answer:

The answer is D-27.00 because you are rounding off to the nearest 100 I hope this helps you

Answer:

C. 26.75

Step-by-step explanation:

26.745 is rounded to 26.75

Answer:

4

Step-by-step explanation:

21 - 4 × ❒ = 5

-4x = 5 - 21

-4x = 16 (divide both sides)

x = 4

Answer:

20

Step-by-step explanation:

100/5=20

Answer:

b

Step-by-step explanation:

Answer:

169

Step-by-step explanation:

x²+26x=23

=> to complete the square, the equation should be : x²+26x + (26/2)² = 23 + (26/2)²

<=> x² +26x + 13² = 23 + 13²

<=> x² +26x +169 = 23 + 169

<=> (x+13)² = 192

so, (x+13)² is the square form , and 169 must be added to complete the square

For 2ab to complete in (a+b)² formula

a=1

So 169 must be added

Answer:  answer is A

A:3/32

B:2/3

C: 1 1/2

D:4

Answer:

(xou)2

Step-by-step explanation:

A yacht is traveling 35° west of south at 15 miles/hour in still water. Find the component form of vector r, which represents the yacht's motion.

Answer:

Step-by-step explanation:

Given polynomial is (-10x + 1).

This polynomial has two terms.

Therefore, it's a binomial with two separate terms.

The expression represents a binomial polynomial with two terms. The constant term is 1, the leading term is -10x, and the leading coefficient is (-10).