A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder?Use the function y=13cos(theta) to find the answer


Answer 1


height = 9.19 ft

Step-by-step explanation:

The ladder is resting on a wall. The angle the ladder makes with the floor is 45°. The ladder is 13 ft. The illustration forms a right angle triangle.

The hypotenuse side of the right angle triangle is 13 ft . The opposite side of the right angle triangle is the unknown which is the height off the ground the top of the ladder. Therefore,

Using ratio

sin ∅ =  opposite/hypotenuse

sin ∅ = opp/13

sin 45° = opp/13

cross multiply

13 sin 45 = opp

opp = 13 × 0.70710678118

opp = 9.19238815543

height = 9.19 ft


You can use the following base on your equation(y = 13 cos ∅)

The other angle will definitely be 45° since total angle in a triangle is 180°. 180 - 90 - 45 = 45°.

The adjacent side of the triangle will be the unknown side if we use cosine ratio.

cos ∅ = adjacent/hypotenuse

cos 45° = adjacent/13

cross multiply

From your equation you represented adjacent as y therefore,

y = 13 cos 45°

y = 13 × 0.70710678118

y = 9.19238815543

y = 9.19 ft (which is the required height)

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Answer: D. 19 Bo; 25 Erica

Step-by-step explanation:

Let x represent the number of yoga classes that Bo teaches in a week.

Let y represent the number of yoga classes that Erica teaches in a week.

Between the two of them, they teach 44 yoga classes each week. This means that

x + y = 44 - - - - - - - - - - -1

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y = 2x - 13

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Penny reads 13 pages in 1/2 hour. What is the unit rate for pages per hour? For hours per page? How many hours per page



13 pages : 1/2 hour Multiply both sides by 2

26 pages : 1 hour ------>> 26 pages/hr

Flip over 26 pages/hr ----->>> hr / 26 pages = 1 hr / 26 pages

Split up the fraction: (1/26) hr / page



Step-by-step explanation:

13 in 1/2 hour



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Argument B: b. weak

Argument C: a. strong

Argument D: a. Strong

Step-by-step explanation:

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Step-by-step explanation:




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Step-by-step explanation:
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Perimeter of a rectangle = 2(l+w) where l is the length and w is the width
Perimeter= 2(81.47 + 34.2)
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  • Question 1. C
  • Question 2. D

Step-by-step explanation:

Question 1

Reflection of point (5, -3) across line y = x is symmetrical point:

  • (x, y) → (y, -x)
  • (5, -3) → (-3, 5)

Correct choice is C

See attached

Question 2

  • Coordinates of A = (4, 3)
  • Coordinates of A' = (-3, 4)

This is 90° counterclockwise or 270° clockwise rotation

  • (x, y) → (-y, x)
  • (4, 3) → (-3, 4)

Correct choice is D


Step-by-step explanation: