SOLUTION: I've been working on this all day. And i need some assistance. Can someone please help me?
A right triangle has legs of lengths 9 and 12
(a) Its hypotenuse has a length of_____
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Question 85405: I've been working on this all day. And i need some assistance. Can someone please help me?
A right triangle has legs of lengths 9 and 12
(a) Its hypotenuse has a length of_______
(b) The altitude to the hypotenuse divides it into segments of lengths___ and ____
(c) The altitude to the hypotenuse has length_____
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
I've been working on this all day. And i need some assistance. Can someone please help me?
A right triangle has legs of lengths 9 and 12
(a) Its hypotenuse has a length of_______
a^2 + b^2 = c^2
a is a side
b is the other side
c is the hypotenuse
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
15 = c
(b) The altitude to the hypotenuse divides it into segments of lengths___ and ____
The altitude strikes the hypotenuse at a right angle. Assume the larger length of the hypotenuse is x and the smaller portion is 15 - x. Knowing your theorm, you should get:
12^2 = (x)15
9.6 = x
You have the lengths: x and 15 - x
You have the lengths: 9.6 and 5.4
(c) The altitude to the hypotenuse has length_____
Knowing your theorm:
h^2 = 9.6 * 5.4
h = 7.2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Since we have a triangle with legs of 9 , 12 and a hypotenuse of x(our unknown side), we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
Plug in a=9 and b=12 and lets solve for c
Square each individual term
Combine like terms
Take the square root of both sides
Simplify
So our answer is
(a) "Its hypotenuse has a length of__15__"
To find the altitude (to the hypotenuse), we can use this formula:
plug in the given info
So the length of the altitude is 7.2
(c) The altitude to the hypotenuse has length___7.2__"
So now construct a smaller triangle within the given one. Now using the altitude's length, we can find one piece of the hypotenuse
Since we have a triangle with legs of x (our unknown side), 7.2 and a hypotenuse of 9, we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
Plug in b=7.2 and c=9 and lets solve for a
Square each individual term
Subtract 51.84 from both sides
Combine like terms
Take the square root of both sides
Simplify
So our answer is
So the length of one piece of the hypotenuse is 5.4. Now subtract 5.4 from 15 to find the other piece's length
So the length of the other piece is 9.6
(b) The altitude to the hypotenuse divides it into segments of lengths_5.4__ and _9.6___
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