How do you calculate the length of one side of a triangle when you have the measurements for two other sides?

Question

No website links please i will not use them - just a simple formula or explanation please.

Side b measures 15 cm, side c measures 6 cm. The question is
the third side of the triangle is 10 cm more than one of the sides and 1 cm more than the other . What is its length?
Please show me step by step how this is worked out so that i can use the formula again.

Also I have another one i am stuck on:
One side of a triangle measures 16 cm and another measures 8 cm. If the area of the triangle is 48 sq cm what is the length of the third side? Again how do i work it out so i know how to do it?

Answer 1

if it is a right triangle than Side A(squared) + Side B(Squared)= Side C(squared)

SO if you know 2 sides are 2cm and 4 cm then it is 4+16=20 then take the square root of 20 and you'll have your answer

Answer 2

hersheba has given the answer to the first part. It is not really a question about triangles, just numbers.

The second question is a little more tricky. You need to know two formulae.

Area of a triangle is half the base times the height.
Pythagorus' theorem for a right triangle as given by others above.

Let's make the side of length 16 the base. We know the area is 48 so half the height must be 3, giving the height at 6.

I suggest you draw a diagram here. Mark off the base. Draw a parallel line 6 above it. Draw a circle at one of the base with radius 8. You will see this circle cuts the upper line in two places. These are the two alternatives for the third point of the triangle.

Completing the triangle you should see that in each possibility you have two right-angled triangles.

Calculate the distance along the base where the height is drawn. This is the square root of (8^2 - 6^2) = sqrt(28)

Now the other right triangle has a base of either 16 minus sqrt(28) or 16 plus sqrt(28)

The third side of the original triangle is, using Pythagorus again, either

sqrt(6^2 + (16+sqrt(28))^2)
or the same calculation subtracting the intermediate answer.

It sounds complicated but is much easier with a diagram.

Answer 3

It depends on whether it's a right angled triangle or not.
If it is, use Pythagoras' theorem;
a2 = b2 + c2. (a2 is 'a squared' etc)
If it's not, you have to use the cosine rule and you must know the size of the angle between your two known sides:
a2 = b2 + c2 - 2bc cos A.
Send me the problem, I will try to do it for you, or help you through it.

Edit...the first one is simple a is 1cm more than b and 10 cm more than c so
15 + 1 = 16 and 6 = 10 = 16. Ans = 16 cm.
You've only got one other option 15+10 = 25 and 6+1 = 7 this does not work.

Tringyokel has the correct method for no2.
The answer = 12.27cm to 2 dp.

Answer 4

A triangle can not have 3 ninety degree angles; it does not be a triangle yet quite a rectangle. Why? All 3 angles of a triangle upload as much as one hundred eighty stages, and ninety * 3 = 270 that's larger than one hundred eighty. i like dr bob's answer; in spite of the undeniable fact that in case you draw a triangle on a sphere that's going to now not be stated as a triangle; a triangle is a 2-d merchandise, and that would make it 3-D.

Answer 5

Part 1
Side B =15cm
Side C = 6cm

Side A = B or C +10 and C or B +1

By simple math the only possible solution for this is 16cm
ie Side B +1 and Side C +10

Answer 6

let the unknown side be called "a"

the two sides that are known (b and c) are 15cm and 6cm respectively

b + c + 10 + 1 = 2a

so

15 + 6 + 10 + 1 = 32

a = 32 / 2 = 16

as others have said, Tringyokel has the second one covered

Answer 7

The answer really depends on the nature of your triangle which is determined by its angles.

- For a triangle with a 90° it is very straight forward you can use pythagore. hypotenus c² =a²+b²
For such a triangle, a/b = tang(angle between b and c)
in such triangle the opposed angles are complementary meaning that their sum equal 90° so cosinus of one angle equal sinus of the other.

Gives me the angles and I will give you the answer

Answer 8

when you know two sides and seek for third you use cosine rule let
side x , side y both known
side z unknown
included angle between x and y shoul be known Z
z^2=x^2 + y^2 - 2.x.y.cosZ
and the included angle SHOULD be known because each time you change it you might find another different third side lenght
good luck

Answer 9

If it is a right triangle you can use a^2 + b^2 = c^2.
If not you need to know a measurement of an angle you could use a trig function Sin Co sin or tang.

Answer 10

if you are given the lengths of two sides of a triangle then find the sum of the two sides and then minus the total length with the sum of the two sides