Find the missing side length to the nearest tenth of a centimeter.
The correct answer and explanation is:
To help you find the missing side length to the nearest tenth of a centimeter, I need a bit more information. Usually, such problems involve:
- A triangle (often a right triangle)
- Two given sides, with the third side missing
- Or, two sides and an angle (SAS or ASA)
- A diagram or specific values
Since no diagram or values are provided, I’ll demonstrate how this works using a common example with a right triangle:
Example Problem:
A right triangle has one leg of 6 cm and another leg of 8 cm. What is the length of the hypotenuse?
Step-by-step Solution Using the Pythagorean Theorem:
In a right triangle, the Pythagorean Theorem applies: a2+b2=c2a^2 + b^2 = c^2
Where:
- aa and bb are the legs
- cc is the hypotenuse (the side opposite the right angle)
Given:
- a=6a = 6 cm
- b=8b = 8 cm
Now plug in the values: 62+82=c2⇒36+64=c2⇒100=c2⇒c=100⇒c=10 cm6^2 + 8^2 = c^2 \Rightarrow 36 + 64 = c^2 \Rightarrow 100 = c^2 \Rightarrow c = \sqrt{100} \Rightarrow c = 10 \text{ cm}
Final Answer:
The missing side length is 10.0 cm.
Explanation (300 Words):
In geometry, determining a missing side in a triangle depends on the type of triangle and the information provided. For right triangles, the Pythagorean Theorem is the most common method. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It’s written as: a2+b2=c2a^2 + b^2 = c^2
This only works when the triangle is a right triangle. If you’re given the two legs of the triangle, you square each, add the results, then take the square root to find the hypotenuse. If instead the hypotenuse and one leg are given, you subtract the square of the known leg from the square of the hypotenuse, then take the square root to find the missing leg.
Precision matters in measurements. Since the question asked for the answer to the nearest tenth of a centimeter, it’s important to round properly after calculating. In our example, the hypotenuse came out exactly to 10 cm, so to the nearest tenth, it is 10.0 cm.
If the triangle was not a right triangle, we would need the Law of Cosines or Law of Sines, depending on the information given. For now, with a right triangle and two legs, the Pythagorean Theorem is the most efficient and reliable method.