find the 3rd side of triangle if...?

Question

the longest side of triangle is 20cm and one of the other side is 10 cm. area of triangle is 80 sqcm.

Answer 1

If x is the angle between the two given sides, then:
80 = 100sin(x)
sin(x) = 0.8
cos(x) = 0.6
If c is the third side, then:
c^2 = 20^2 + 10^2 - 400cos(x)
c = sqrt(260) cm.

Answer 2

16

Answer 3

80/20 = 4 = h/2
h = 8
100 - 64 = 36
20 - 6 = 14
64 + 196 = 260
√260 ≈ 16.12452

80/10 = 8
h = 16
400 - 256 = 144
12 - 10 = 2
4 + 256 = 260
√260 ≈ 16.12452

Answer 4

80/20 = 4 = h/2
h = 8
100 - 64 = 36
20 - 6 = 14
64 + 196 = 260
√260 ≈ 16.12452

80/10 = 8
h = 16
400 - 256 = 144
12 - 10 = 2
4 + 256 = 260
√260 ≈ 16.12452

Answer 5

Let us use Heron's formula. Let the third side be x cm. Now,
s=(10+20+x)/2
therefore,
80=square root of{s(s-20)(s-10)(s-x)}
squaring both sides
6400={s(s-20)(s-10)(s-x)}
=[{s}{(30+x)/2} -20] [{(30+x)/2} -10] [{(30+x)/2} -x]
=[{s}{(x-10)/2} {(x+10)/2} {(30-x)/2}]
=s{(x^2-100)(30-x)}/8
={(30+x)(x^2-100)(30-x)}/16
=> 0={(900-x^2)(x^2-100)} + 102400
solve it for x and you will get the answer.

Answer 6

You use Heron's Formula to solve this.

You set an equation where s= half the sum of (10+20+x)

and the area, 80 is the square root of the product of s(s-10)(s-20)(s-x).

You plug in S in the equation and solve for x.

Answer 7

Approx. 16 cm

Answer 8

40 cm

Answer 9

u use the herons formula to answer this question and get the answer as 16

Answer 10

it is 16 the answer is derived from the formula area=1/2*height*base