https://file.aiquickdraw.com/mathbot/file/17310352416320iwpxgh0.jpg

The image shows a right triangle with a car positioned on the hypotenuse. The height (opposite side) is labeled as \( 3 \) units, the base (adjacent side) as \( 10 \) units, and the hypotenuse (which the car is on) is unknown and marked with a question mark.

To find the length of the hypotenuse, we can use the Pythagorean theorem:

\[
a^2 + b^2 = c^2
\]

where:
- \( a = 3 \),
- \( b = 10 \),
- \( c \) is the hypotenuse.

Plugging in the values:

\[
3^2 + 10^2 = c^2
\]
\[
9 + 100 = c^2
\]
\[
c^2 = 109
\]
\[
c = \sqrt{109}
\]
\[
c \approx 10.44
\]

So, the length of the hypotenuse is approximately \( 10.44 \) units.

Would you like further details or have any questions?

Here are some related questions:
1. How would you find the angle of elevation of the road?
2. What would happen if the height was doubled while keeping the base the same?
3. How could you apply trigonometric functions to find the angle in this triangle?
4. If the car weighs a certain amount, how would you calculate the force along the incline?
5. How would you find the area of this triangle?

**Tip:** Remember, the Pythagorean theorem only applies to right triangles.

Find the length of the hypotenuse in a right triangle where the opposite side is 3 units, the adjacent side is 10 units, and the hypotenuse is unknown.

Learn how to calculate the length of the hypotenuse in a right triangle using the Pythagorean theorem. In this example, the opposite side is 3 units, the adjacent side is 10 units, and the hypotenuse is unknown. Suitable for students in Grades 8-10.

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