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Semenov [28]
2 years ago
10

Can some show the steps and the answer please I really need help tell me how you get it and the answer

Mathematics
1 answer:
Tems11 [23]2 years ago
5 0

Answer:

Step-by-step explanation:

here is some helpful trig function reminders.. copy this and keep it

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

they ask how long is the ladder

they give us the opposite side (8) and the adjacent side (6)  

and the Hyp is the length of the ladder.   They expect you to sort this out in your head.  :/  

there is two steps .. we'll solve for the angle.. then we can use that to find the Hyp side..(long side of triangle)  which is the ladder length

Tan(Ф) = Opp / Adj

Tan(Ф) = 8 / 6

Ф = arcTan(8 / 6)

Ф ≈ 53.130°

now lets use that angle with one of the other trig functions to find the Hyp.. sin or cos will work b/c we have both the opp and the adj sides lengths.  let's use cos

Cos(53.130) = 6 / Hyp

Hyp = 6 / Cos(53.130)   ( I just used algebra to swap the two)

Hyp = 9.99997

the ladder will be 10' long.  

ask in the comments if you need any more explaining  

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The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

<h3>What is the area of the equilateral, isosceles and right angle triangle?</h3>

Note that:

The area of an Equilateral triangle is expressed as A = ((√3)/4)a²

Where a is the dimension of the side.

The area of an Isosceles triangle is expressed as A = (ah)/2

Where a is the dimension of the base and h is the height.

The area of a Right angled triangle is expressed as A = (ab)/2

Where a and b is the dimension of the two sides other than the hypotenuse.

For the Equilateral triangle.

Given that;

  • a = 5.4mm
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A = ((√3)/4)(5.4mm)²

A = ((√3)/4)( 29.16mm² )

A = 12.6mm²

Area of the Equilateral triangle is 12.6mm²

For the Isosceles triangle.

Given that;

  • Base a = 3.4in
  • Slant height b = 5.9in
  • height h = ?
  • Area A = ?

The height h is the imaginary line drawn upward from the center of a.

First, we calculate the height using Pythagorean theorem

x² = y² + z²

Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h

(5.9in)² = (1.7in)² + h²

34.81in² = 2.89in² + h²

h² = 34.81in² - 2.89in²

h² = 31.92in²

h = √31.92in²

h = 5.65in

Now, the area will be;

A = (ah)/2

A = (3.4in × 5.65in )/2

A = 19.21in²/2

A = 9.61in²

Area of the Isosceles triangle is 9.61in².

For the Right angled triangle

Given that;

  • a = 8.2yds
  • b = 4.1yds
  • c = 9.17yds
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A = (ab)/2

A = ( 8.2yds × 4.1yds)/2

A = ( 33.62yds²)/2

A = 16.81yds²

Area of the Right angled triangle is 16.81yds²

Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.

Learn more about Pythagorean theorem here: brainly.com/question/343682

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