Herman is making a small triangular table. If two of the sides will measure about 25 inches each, how many inches should the longest side (c) measure? Use the appropriate formula and round your answer to the nearest tenth.
I don't know how to do this cuz it doesn't tell me if it's a right triangle or not. HELP!
would the long side be 36 in?
I think they are after the property that in
any triangle, the sum of any two sides must be greater than the third side, or else you cannot produce the triangle.
e.g. I cannot draw a triangle with sides 3,4, and 9
So the third side must be < 50
What was the "appropriate formula" they are talking about?
I think we have to assume it's either a right or equilateral triangle.
Using the Pythagorean Theorem, I get 35.3553 = 35.6 inches.
Correction: 35.4 inches
To solve this problem, you can use the Law of Cosines to find the length of the longest side (c) of the triangle.
The Law of Cosines states that, in any triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of the lengths of those two sides times the cosine of the included angle.
In this case, since we don't have the included angle, we need to assume that it is less than 180 degrees, making it a non-obtuse triangle (not right triangle). That means the longest side will be opposite the largest angle.
Here's how to find the length of the longest side (c):
1. Identify the two sides given: 25 inches each.
2. Assume one of these sides as the longest (c), and the other as a and b (order doesn't matter).
3. Apply the Law of Cosines: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle opposite to the longest side.
4. Rearrange the formula to solve for c: c = sqrt(a^2 + b^2 - 2ab * cos(C)).
5. Plug in the values: a = b = 25 inches.
6. Solve for c using a calculator or an algebraic software, rounding to the nearest tenth.
Note: If you want to find the length of the longest side in a right triangle, you can use the Pythagorean theorem, not the Law of Cosines.