Question 283080: The sides of a triangle are 30,70,and 80 units .if an altitude is dropped upon the side of length 80, then the length of the larger segment cut off on this side is
A 61 units b 62 units c 63 units d 64 units e 65 units
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! The sides of a triangle are 30,70,and 80 units .if an altitude is dropped upon the side of length 80, then the length of the larger segment cut off on this side is
A 61 units b 62 units c 63 units d 64 units e 65 units
Here's an approach:
1. Use Heron's formula to calculate the area from the semi-perimeter S=180/2= 90. The area will be sqrt(s*(s-70)*(s-30)*(s-80)).
2. We can then calculate the height from the formula for the area of a triangle as (80*h)/2 and setting this area equal to the area calculated from 1 and solving for h.
3. Let x and 80-x be the two segments created by the altitude on the side with length 80. Then, using the Pythagorean Theorem, we can calculate the two segments using 70^2 = (80-x)^2 + h^2 and 30^2 = x^2 + h^2.
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