Angle hypotenuse right triangle

The Pythagorean Theorem states for a right triangle
A squared + B squared = C squared
where C is the hypotenuse.

if the hypotenuse is 5cm, then the remaining sides have to be 3cm & 4cm

Also called the 3,4,5 right triangle.

In any right angled triangle, for any angle:

1. The sine of the angle = the length of the opposite side. the length of the hypotenuse.
2. The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
3. The tangent of the angle = the length of the opposite side. the length of the adjacent side.

a^2 + b^2 = c^2
a squared + b squared = c squared, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides in a right-angled triangle.

https://www.youtube.com/watch?v=CAkMUdeB06o

Hi David:
You've got me confused.
A triangle has 3 sides. You have provided 4 lengths and no picture.
The hypotenuse is joins the 2 sides that are the "legs" of the right angle.
The length of the hypotenuse is the square root of the sum of the squares of the sides.
Just apply the "rule" to the appropriate dimensions.
Cheers

The formula to calculate the hypotenuse of a right angled triangle is a^2 + b^2 = c^2 or in words, a squared plus b squared is equal to c squared. The most common mistake is that students make the hypotenuse a squared or b squared. The hypotenuse has to be c squared. Thus, when figuring out the sides of a right-angled triangle, always make sure the hypotenuse is the longest side.

For example, a triangle with sides of length 3 and 4, calculate the hypotenuse. Let a be 3 and b be 4. 3^2 + 4^2 = c^2 or 9+16 = c^2, or 25 = c^2. Now take the square root of both sides and we get c = 5.

Assuming that the angle at A is the right angle, Pythagoras' theorem says that the length of the hypotenuse (the side opposite the right angle) is the square root of the sum of the squares of the other two sides. In your case, AB and AC are 'the other two sides' and BC is the hypotenuse, so:

/ 2 2 /
length BC = V 10 + 20 = V 100 + 400


= V 500 = 22.36 cm

(To find the angle at C, you need trigonometry and is arc-tan(10/20)

and the angle at B is arc-tan(20/10) - 26.5 deg and 63.5 deg)

About 3.54 cm (the square root of 12.5).

x = 6

Yes, there is shortcut because this is right triangle, so you can use Pythagorean theorem (see picture).

1. Length of hypotenuse is square root of sum of squares of lengths of other two sides of triangle, which is equal to square root of 30^2+10^2=31.6 cm.
2. Sin(a)=longer cathetus/hypotenuse=0.949 so a=arcsin(0.949)=71.6 degrees
3. Finally b=90-a=18.4 degrees.

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Formulas relating to right angled triangles are:
Sine = perpendicular divided by hypotenuse
Cosine = base divided by hypotenuse
Tangent = perpendicular divided by base
Sine Tangent and Cosine functions are all available in Excel