A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot

Guest Apr 3, 2019

#1**0 **

We can compare this problem to a puthagreom therom problem. We will be using the formula a^2+b^2=c^2

So we know that the trees hight a, and the the grounds distance b, form a right angle with the ropes legnth, c.

Since there is a 45 degree angle, and there is a right angle, 90 degrees, we add these together and subtract them from 180 since a triangle has a total of 180 degrees through its 3 angles. This gets us 45 degrees.

From that we know that a and b will be equal, since their angles are equal.

a^2+b^2=c^2

We put the values we know into the equation to get a^2+b^2=100^2=10,000

Since a and b are equal, we can simplify to get 2*(a^2)=10,000

Divide both sides by 2 to get a^2=5000

Find the square root of both sides to get a equals the square root of 5000.

The top of the treehouse is at the square root of 5000 feet, rounded to the nearest 10th of a foot, is 70.7 feet.

Hope this helps!

Oh and this isnt geometry/trig this is pre-algebra

IAmJeff Apr 3, 2019

#2**+2 **

Another way to find that height is to use the TRIG sine function.

It's necessary to posit that the tree is perpendicular to the ground, i.e., forms a 90^{o} angle.

The sine of an angle in a right triangle is the opposite side over the hypotenuse.

So, sin 45^{o} = x/100 where x is the height of the treehouse and 100 is the length of the rope

You have to look up the value for the sin 45^{o} which we find to be 0**.**7071.

So, plugging in that value for the sine: 0**.**7071 = x/100

I just happen to prefer the unknown on the left, so I turn it around: x/100 = 0**.**7071

Multiply both sides by 100: x = 100 times 0**.**7071

x = 70**.**7 feet

That's a pretty doggone high treehouse.

.

Guest Apr 3, 2019

#3**0 **

sin 45 = opp/ hypotenuse Hypotenuse is 100 ft rope opp= height

.707 = opp/100

70.7 ft = opp = height

ElectricPavlov Apr 3, 2019