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# Building a Ski-ramp

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Write an inequality in the variable x for the degree measure of the smallest angle of a triangle given that the degree measure of the smallest angle is at most 30 degrees

diagram
top angle x+8
bottom left x
right angle has ?

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https://brainmass.com/math/triangles/building-a-ski-ramp-373419

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The third angle in the given triangle = 180Â° - (x + x + 8) = 180Â° - 2x - 8Â° = 172Â° - 2x
We know that for any positive value of x, x < x + 8
Now consider x and 172 - 2x
Depending upon the value of x, either x becomes the smallest angle or 172 - 2x becomes the smallest angle
(a) Assuming x to be the smallest angle, the inequality is obviously 0 < x â‰¤ 30
(b) Assuming 172 - 2x to be the smallest angle, the inequality is 0 < 172 - 2x â‰¤ 30
172 - 2x > 0
172 > 2x
2x < 172
x < 86
Again, 142 â‰¤ 2x
2x â‰¥ 142
x â‰¥ 71
So, assuming 172 - 2x to be the smallest angle, the inequality is 71 â‰¤ x < 86
Answer: {x | 0 < x â‰¤ 30 or 71 â‰¤ x < 86}

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Â© BrainMass Inc. brainmass.com December 24, 2021, 9:23 pm ad1c9bdddf>
https://brainmass.com/math/triangles/building-a-ski-ramp-373419