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# The sides of a triangle are 14 cm, 48 cm and 50 cm.

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The sides of a triangle are 14 cm, 48 cm and 50 cm. The perpendicular distance from the longest side to the midpoint of the shortest side is, in cm? (perpendicular to longest side)

Oct 29, 2017

#1
+7348
+1

We want to find  x .

First let's find  cos a  using the law of cosines:     c2  =  a2 + b2 - 2ab cos C

482  =  142 + 502 - 2(14)(50) cos a

2304  =  196 + 2500 - 1400 cos a

-392  =  -1400 cos a

0.28  =  cos a

And using the Pythagorean identity

0.282 + sina  =  1

sin2 a  =  0.9216

sin a  =  0.96

Now....let's just look at the little triangle.

sin a  =  opposite / hypotenuse

sin a  =  x / 7

0.96 =  x / 7

7 * 0.96  =  x

6.72  =  x

Oct 29, 2017
edited by hectictar  Oct 29, 2017

#1
+7348
+1

We want to find  x .

First let's find  cos a  using the law of cosines:     c2  =  a2 + b2 - 2ab cos C

482  =  142 + 502 - 2(14)(50) cos a

2304  =  196 + 2500 - 1400 cos a

-392  =  -1400 cos a

0.28  =  cos a

And using the Pythagorean identity

0.282 + sina  =  1

sin2 a  =  0.9216

sin a  =  0.96

Now....let's just look at the little triangle.

sin a  =  opposite / hypotenuse

sin a  =  x / 7

0.96 =  x / 7

7 * 0.96  =  x

6.72  =  x

hectictar Oct 29, 2017
edited by hectictar  Oct 29, 2017