Mathematics, 09.01.2020 00:31 Pointjazzyqueen602

Aladder 8ft long resting against a house makes a 60 degree
angle with the ground. how far up does the house reach? give answer
in terms of radicals with the radical in the numerator.

Answers: 3

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Answer from: sergiog6833

4√3 feet

Step-by-step explanation:

Here, a ladder is resting against a house makes a 60° with the ground,

Consider x be the distance of the top of ladder from the foot of house and y be the distance of bottom of ladder from the house. ( shown in the below diagram )

Using trigonometric ratio,

$\sin 60^{\circ}=\frac{\text{Distance of top of ladder from the bottom of house}}{\text{Length of ladder}}$

We have, length of ladder = 8 ft,

$\sin 60^{\circ}=\frac{x}{8}$

$\frac{\sqrt{3}}{2}=\frac{x}{8}$

$8\sqrt{3} = 2x$

$4\sqrt{3}=x$

Hence, the house would reach 4√3 feet up.

Aladder 8ft long resting against a house makes a 60 degree angle with the ground. how far up does th

Answer from: Quest

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1