+279 A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? Explain.
+576 This is an extention of the pythagorean theorem.
lets take the two smaller side lengths, square them, and add them together. Then we will compare with the longest side squared to see if it fits the pythagorean theorem.
7^2 +10^2 =49+100=149
15^2=225
since 225 is not equal to 149 we have shown that this is not a right triangle. Well then what is it!?
if we look closely at the form a^2+b^2=c^2 we see that in our case the right side of the equation is greater than the left side. What this means is that the side that would have been the hypotenuse were this a right triangle is too long for it to be a right triangle. That means that the angle which would normally be a right angle must be greater than a right angle to create this side which is longer than what they hypotenuse would need to be. Therefore, it must be the case that this is an obtuse triangle.
Please note that if the part of the equation that is c^2 were less than the a^2+b^2 side then it would be acute.
+279
| A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles.
|
+576 This is an extention of the pythagorean theorem.
lets take the two smaller side lengths, square them, and add them together. Then we will compare with the longest side squared to see if it fits the pythagorean theorem.
7^2 +10^2 =49+100=149
15^2=225
since 225 is not equal to 149 we have shown that this is not a right triangle. Well then what is it!?
if we look closely at the form a^2+b^2=c^2 we see that in our case the right side of the equation is greater than the left side. What this means is that the side that would have been the hypotenuse were this a right triangle is too long for it to be a right triangle. That means that the angle which would normally be a right angle must be greater than a right angle to create this side which is longer than what they hypotenuse would need to be. Therefore, it must be the case that this is an obtuse triangle.
Please note that if the part of the equation that is c^2 were less than the a^2+b^2 side then it would be acute.
+118687 hi Natasha,
The sides are 10,15 and 7
The largest angle is opposite the longest side. You can use cosine rule to work this out.
You don't need to go all the way. If cos(angle) is positive then it is an acute angle and if neg then it is an obtuse angle.
Either way, the other 2 have to be acute angles.
You can finish it can't you Natasza?
Post again if you have problems.
