To solve this problem, let's break it down step-by-step.
1. Understand the Problem: We need to find the ratio of the hypotenuse to the leg in a right-angled triangle where each leg is 2 units long.
2. Recall the Pythagorean Theorem: For a right-angled triangle, the relationship between the legs [tex]\( a \)[/tex] and [tex]\( b \)[/tex], and the hypotenuse [tex]\( c \)[/tex], is given by:
[tex]\[
c = \sqrt{a^2 + b^2}
\][/tex]
3. Substitute the known values: Here [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are both 2 units.
[tex]\[
c = \sqrt{2^2 + 2^2}
\][/tex]
4. Calculate the squares:
[tex]\[
c = \sqrt{4 + 4} = \sqrt{8}
\][/tex]
5. Find the square root:
The square root of 8 is approximately:
[tex]\[
\sqrt{8} \approx 2.828
\][/tex]
(more accurately, [tex]\( \sqrt{8} \approx 2.8284271247461903 \)[/tex])
6. Find the ratio: To get the ratio of the hypotenuse to one leg, we divide the length of the hypotenuse by the length of one leg:
[tex]\[
\text{Ratio} = \frac{2.828}{2} \approx 1.414
\][/tex]
(more precisely, [tex]\( \frac{2.8284271247461903}{2} \approx 1.4142135623730951 \)[/tex])
7. Consider the Options: Given the multiple-choice options:
- 1.4
- 2.0
- 2.8
We can see that the calculated ratio (approximately 1.414) is closest to 1.4.
Conclusion:
The ratio of the hypotenuse to the leg when the leg length is 2 units is approximately 1.4. Therefore, the correct answer is 1.4.
