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# ​ Help 4

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Help

Jul 14, 2020

#1
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By Heron's formula, the area of the triangle is 90.  So the shortest altitude, which is opposite the longest side, is 2*90/26 = 90/13.

Jul 14, 2020
#2
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Please check you work, this is not correct

qwertyzz  Jul 14, 2020
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Heron's formula is $$\sqrt{s(s-a)(s-b)(s-c)}=area$$ where s is the semi-perimeter (in less fancy words $$\frac{area}{2}$$) and a, b, c are the sides of the triangle. I'm pretty sure the guest did something wrong in the calculations there and that is why he/she was wrong

amazingxin777  Jul 14, 2020
#3
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Right scalene triangle.

Sides: a = 10   b = 24   c = 26

Area: T = 120
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 22.62° = 22°37'11″ = 0.395 rad
Angle ∠ B = β = 67.38° = 67°22'49″ = 1.176 rad
Angle ∠ C = γ = 90° = 1.571 rad

Height: ha = 24
Height: hb = 10
Height: hc = 9.231 ==[2 x 120] / 26 ==9.231 - The shortest altitude.

Jul 14, 2020
#4
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My textbook doesn't accept rounded answers

qwertyzz  Jul 14, 2020
#5
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What was the purpose of writing [2 x 120] / 26 =240 / 26 at the bottom? Can you read at all??

Guest Jul 14, 2020
#7
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240 / 26 = 9.230769231

Dragan  Jul 15, 2020
#8
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Thank you!

qwertyzz  Jul 15, 2020