How would you find a missing measurement of a triangle?

Question

For example, the is a triangle woth a side of 30 cm, and a base of 21 cm, and side xcm. How would you find side x?

note: side x cm is the height.

Answer 1

If and only if your triangle is a Right angle triangel (has one 90 o angle) you can use pythagoras' theorem which states

a^2 + b^2 = c^2 where c is the length of the longest side (opposite the right angle) and a and b are the other sides.

If you don't have a right angle, you need to know at least one angle.

Then you can use the Law of cosines:
c^2 = a^2 + b^2 - 2abCos (angleC) (google it for a picture)

or the law of Sines:
Sin A/a = Sin B /b = Sin C/c.

:)

Answer 2

Make a diagram with the measurements you know. If the base is 21 cm and you're trying to find either the height of the triangle or the third side, you have all the info you need. The height is a line that bisects the triangle and begins at the mid-point of base and goes up to the angle at the top of the triangle. That line creates a right angle on either side of the base. That means that you now have two "right triangles." Do you know the Pythagorian Theorem, c-squared = a-squared + b=squared? You can use that because you have two right triangles. According to you, c=30 cm. Since the base was bisected, b = 1/2 x the base, i.e., 1/2 of 21. You now have c & b. Solve for a. That'll give you the height. If you want to know the measurement for the third side, you now have 2 sides in the second triangle: a & b. Solve for c using the formula above. Good Luck!

Answer 3

You added that side xcm is the height. Without that information there are an infinate number of answers, or none. So if side "x" is the height you now can have a simple right triangle with the hypotenus being the longest side or 30.
The two sides are 21 which is the base and vertical side "x"
Using pythagorean theorm solve for "x"
30^2=21^2 + x^2 x= 21.4cm

Answer 4

from the figure find out the hypotenuse of the traingle (i.e.) the longest side.

if the unknown side is the hypotenuse of the triangle then its equal to,
x = sqrt(30*30+21*21)
= sqrt 1341
= 36.62 cm

if its not the hypotenuse then it is equal to,
x = sqrt(30*30-21*21)
= sqrt 459
= 21.42 cm

Answer 5

x is the height of the triangle or the length of the unknown side?

Answer 6

A RIGHT triangle? Pythagorean theoram.

Answer 7

add together they = 180 so

180-
51
------
???

that's your answer!