The altitude to the hypotenuse of a right triangle divides the hypotenuse into 15 inches and 30 inch segments. Explain or show how to find the exact length of the altitude including the correct value. Then explain or show how to find the length of each leg including the correct values.
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A right triangle has one leg with unknown length, the other leg with length of 5 m, and the hypotenuse with length 13 times sqrt 5 m.
We can use the Pythagorean formula to find the other leg of the right triangle.
Where a and b are the legs of the triangle and c is the hypotenuse.
According to the given problem,
one leg: a= 5m and hypotenuse: c=13√5 m.
So, we can plug in these values in the above equation to get the value of unknown side:b. Hence,
25 + b² = 13²*(√5)²
25 + b² = 169* 5
25+ b² = 845
25 + b² - 25 = 845 - 25
b² = 820
b =√ 820
b = √(4*205)
b = √4 *√205
b = 2√205
b= 2* 14.32
b = 28.64
So, b= 28.6 (Rounded to one decimal place)
Hence, the exact length of the unknown leg is 2√205m or 28.6 m (approximately).
A right triangle, one leg is 5 meters, one leg is unknown, and the hypotenuse is 11 meters.
Use the Pythagorean Theorem, since this is a right triangle. If a and b are sides and c is the hypotenuse, then c^2 = a^2 + b^2.
Subbing the given side lengths, c^2 = (5 m)^2 + (11 m)^2 = 25 m^2 + 121 m^2, or
146 m^2. Thus, the length of the hypotenuse, c, is √(146 m^2), or 12.08 m, to two decimal places.
A right triangle, one leg is 8 millimeters, one leg is 8.1 millimeters, and the hypotenuse is unknown. Again, use the Pyth. Thm.:
(8.1 mm)^2 + (8 mm)^2 = c^2 = square of the length of the hypotenuse.
Then c^2 = 129.61 mm^2. This is not a perfect square, so we can ony give an approximate value for the hypo length, c: √(129.61 mm^2) or 11.38 mm.
The hypotenuse of an isosceles right triangle is 11 centimeters longer than either of its legs. find the exact length of each side.
Let the hypotenuse be y and the other legs be x.
Determine the exact dimension of the triangle
Using Pythagoras theorem;
Collect like terms
Using quadratic formula:
x can not be negative.
Hence, the dimensions are:
The hypotenuse, opposite side and adjacent side of a right angle triangle are related by the Pythagoras theorem which states that
Hypotenuse ^2 = opposite^2 + adjacent ^2
The hypotenuse of an isosceles right triangle is 2 feet longer than either of its legs. Let x represent the length of the hypotenuse. Then
Either of the other sides is x - 2.
Applying Pythagoras theorem
x^2 = (x - 2)^2 + (x - 2)^2
x^2 = x^2 - 2x - 2x + 4 + x^2 - 2x - 2x + 4
x^2 = x^2 + x^2 - 4x - 4x+ 4 + 4
x^2 = 2x^2 - 8x+ 4 + 4
2x^2 - x^2 - 8x + 8 = 0
x^2 - 8x + 8 = 0
For quadratic formular,
x = -b ±√b^2 - 4ac]/2a
a = 1
b = -8
c = 8
x = [- - 8±√-8^2 - 4× ×1×8]/2×1
x = [8 ±5.66]/2
x = 8 + 5.66]/2 or x = (8 - 5.66)/2
x = 13.66/2 or x = 2.34/2
x = 6.83 or x = 1.17
The hypotenuse is 6.83
Either of the other sides are 6.83 - 2 =4.83
The exact length for each side is 6.36.
I used a calculator.
Hypotenuse of an right angle isosceles triangle is 11centimeters longer than the length of each side.
So Let, the sides of the isosceles right angle triangle are x,x, 11+x
In a right angle triangle
hypotenuse^2 = Side ^2 + side ^2
(11+x)^2 = x^2 +x^2
So the sides are 26.5,26.5 and 37.5