Please help with trig problem!!

[Cp0699]

I am in Trigonometry and in 10th grade.
A ladder leaning against a house makes an angle of 75 degrees with the ground. When the ladder is moved 4 feet further from the house, it makes an angle of 65 degrees with the ground. To the nearest hundredth of a foot, how far does the ladder slide down a house?

 

[Ishuda]

A ladder leaning against a house makes an angle of 75 degrees with the ground. When the ladder is moved 4 feet further from the house, it makes an angle of 65 degrees with the ground. To the nearest hundredth of a foot, how far does the ladder slide down a house?

Let a be the height of the ladder and b be the distance from the house of the base of the ladder when the ladder makes a 75º angle with the house. What is the relationship between a and b?

Let x be the distance the ladder moves down the house when the ladder makes a 65º angle with the house. What is the relationship between a-x and b+4?

What is the relationship between L (the length of the ladder) and a?

What is the relationship between L and a-x?

If you write down all of these relationships, it will give you enough information to solve for x.

 

[Deleted member 4993]

A ladder leaning against a house makes an angle of 75 degrees with the ground. When the ladder is moved 4 feet further from the house, it makes an angle of 65 degrees with the ground. To the nearest hundredth of a foot, how far does the ladder slide down a house?

Hint: draw a sketch and assume that the length of the ladder = L

The first time

height along the wall = h₁ → h₁ = L * sin75°

Distance along the floor = d₁ → d₁ = L * cos75°

The second time

height along the wall = h₂ → h₂ = L * sin65°

Distance along the floor = d₂ → d₂ = L * cos65°

and

d₂ - d₁ = 4

h₁ - h₂ = ?

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