geometry
posted by samuel .
Two sides of a triangle measure 8 and 15. How many integer values can be assigned to the third side so that all the angles in the triangle are acute?

The cosine rule gives the formula for the cosine of an angle when the three sides are known:
cos(A)=(B²+C²A²)/(2BC)
where B and C are lengths of sides adjacent to A.
We know that a positive angle is acute when cos(A) is positive, which in turn requires that
B²+C²A²>0 ....(1)
So if all three angles of a triangle have to be acute, we have the two additional requirement analogous to (1) above:
C²+A²B²>0
A²+B²C²>0
If the third side can be chosen such that all three conditions are satisfied, the triangle has acute angles.
Respond to this Question
Similar Questions

Math(geometry)
I need to know how to find the meausure of a triangle using vertical angles, and also how to measure a triangle using linear pairs... Oh, I hope I'm not too late with an answer for you... To measure a triangle using linear pairs, you … 
Geometry
1. The sides of a triangle have lenghts x, x+4, and 20. Specify those values of x for which the triangle is acute with the longest side 20. 2. use the information to decide if triangle ABC is acute, right, or obtuse. AC=13, BC= sq. … 
geometry
Two sides of a triangle measure 2x – 4 and 7x – 2 units, respectively. Which of these is a possible length for the third side of the triangle? 
MATH
two sides of a triangle measure 8 and 15. how many integer values can be assigned to the third side so that all the angles in the triangle are acute. 
geometry
find the value of x in each triangle: triangle x has 1 angle at 53 degree for value x i got: 63.5 degree is that correct? 
geometry
find the value of x in each triangle: triangle x has 1 angle at 53 degree for value x i got: 63.5 degree is that correct? 
Math
True or false and if false write a true statement 1. A right triangle has three right angles. 2. A triangle that has three sides of the same length is an equilateral triangle. 3. An obtuse triangle has two angles that are acute. 4. … 
Math
Write whether the statement is true or false. If false write a true statement. 1. A right triangle has three right angles. False a right triangle has 1 right angle 2. A triangle that has three sides of the same length is an equilateral … 
geometry
Triangle DEF contains two congruent acute angles. The sum of the measures of the two congruent acute angles is greater than 90 degrees. Anna concludes that the triangle must be an acute triangle. Which best describes her conclusion? 
math plz check ;;
A triangle has sides of lengths 5 cm, 5 cm, and square root 47cm. Which of the following statements is true?