Geometry

# What is the length of the hypotenuse of a right triangle that has a base of 5 inches and a height of 12 inches?

###### Wiki User

###### August 16, 2008 11:49AM

In any right triangle, the hypotense squared = the square of one
side + the square of the other side. h2 = a2 + b2 Here, h2 = 52 +
122 = 25 + 144 = 169 We have h2 = 169 The square root of 169 is 13,
so the length of the hypotenuse is **13 inches**.

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### How can you find the base of a right triangle when you have the height and hypotenuse?

The square of the length of the base plus the square of the
length of the height will equal the square of the length of the
hypotenuse of your right triangle, per Pythagoras. Square the
hypotenuse, subtract the square of the height, and then find the
positive square root of that and you'll have the base of your right
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###### Asked in Algebra, Geometry, Roman Numerals

### Can you find the length of the hypotenuse of a right angled triangle with an area of XXIIII square inches and a height of VIII inches giving details of your work?

First find the length of the base: base = area times 2 divided
by height base = 24 times 2 divided by 8 = 6 inches Then use
Pythagoras' Theorem to find length of the hypotenuse: base2 +
height2 = hypotenuse2 62 + 82 = 100 square inches. Square root of
100 = 10 inches. Therefore the length of the hypotenuse is X
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### How do you find the height of an equilateral triangle if you have the length of the hypotenuse?

An equilateral triangle hasn't a hypotenuse; hypotenuse means
the side opposite the right angle in a right triangle. An
equilateral triangle has no right angles; rather all three of its
angles measure 60 degrees. Knowing the length of the hypotenuse of
a right triangle does not give enough information to determine the
triangle's height. But the length of a side (which is the same for
every side) of an equilateral triangle is enough information from
which to calculate the height of that triangle. The first way is
simply to use the formula that has been developed for this purpose:
height = (length X sqrt(3)) / 2. But you can also use the geometry
of right triangles to solve for the height. That is because you can
bisect the triangle with a vertical line from the top vertex to the
center of the base. The length of that line, which splits the
equilateral triangle into two right triangles, is the height of the
equilateral triangle.
We know a lot about each right triangle formed by bisecting the
equilateral triangle: * - The hypotenuse length is the length of
the equilateral triangle's side. * - The base length is half the
length of the hypotenuse. * - The angle opposite the hypotenuse is
90 degrees. * - The angle opposite the vertical is 60 degrees (the
measure of every angle of any equilateral triangle). * - The angle
opposite the base is 30 degrees (half of the bisected 60-degree
angle). * - (Note that the sum of the angles does equal 180
degrees, as it must.) Now to solve for the height of a right
triangle. There are a few ways. For labeling, let's let h=height of
the equilateral triangle and the vertical side of the right
triangle; A=every angle of the equilateral triangle (each 60o);
s=side length of any side of the equilateral triangle and thus the
hypotenuse of the right triangle.
Since the sine of an angle of a right triangle is equal to the
ratio of the opposite side divided by the hypotenuse, we can write
that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig
tables you can now easily find the height.

###### Asked in Math and Arithmetic, Algebra, Geometry

### The demension of a right trapezoid-shaped figure has bases of 28 inches and 16 inches and the slant height is 17 inches What is the lenght in inches of the height?

If you draw another altitude parallel to the height (the side
which is perpendicular to the bases) of the trapezoid, you can see
that a right triangle is formed.
In this triangle the hypotenuse length is 17 in, and the base
length equals to 28 - 16 = 12 in. From the Pythagorean theorem,
height length = √(17 - 12) ≈ 12 in.
Or find the measure of the angle (call it A) opposite to the height
such as:
cos A = 12/17
A = cos-1 (12/17) ≈ 45⁰, which tells us that this right triangle is
an isosceles triangle.
Therefore, the height is (congruent with base) 12 inches long