A 12 ft ladder leaning againist a house make a 64 degree angle with the ground will the ladder reach a window till that is 10.5
ft up from the base of the house?
1 answer:
In triangle ABC
AC = hypotenuse = length of ladder = 12 ft
BC = opposite = height on the wall of house = h
θ = angle of the ladder with the horizontal = 64 deg
using trigonometric formula
Sinθ = opposite/hypotenuse
Sinθ = BC/AC
Sinθ = h/L
Sin64 = h/12
h = 12 Sin64
h = 10.8 ft
since h > 10.5 ft (height of the window)
hence the ladder reach well above the window
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Answer:
Gina is 12 years old
Step-by-step explanation:
First, we will have to write these statements mathematically and then solve.
Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.
The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)
The next statement "Gina's brother is half Gina's age" can be mathematically written as y = ---------------------------------------(2)
Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)
We can now proceed to solve;
Substitute equation (1) and equation(2) into equation (3)
x + y + z = 42
x + + 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
=
x = 12
Therefore, Gina is 12 years old