Examkin

Question

Difficulty: EasyPythagorean Theorem Word Problems

A wooden ramp used for moving equipment is 17 feet long. If the horizontal distance from the base of the ramp to the building is 15 feet, what is the vertical height of the top of the ramp?

  1. A
    2 feet
  2. 8 feetAnswer
  3. C
    32 feet
  4. D
    64 feet

Answer

8 feet
The scenario describes a right triangle where the ramp is the hypotenuse, and the distance to the building is one of the legs. Using the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2. Plugging in the knowns gives 152+b2=17215^2 + b^2 = 17^2, which evaluates to 225+b2=289225 + b^2 = 289. Subtracting 225 from both sides yields b2=64b^2 = 64. The square root of 64 is 8, so the ramp reaches a vertical height of 8 feet.

Step-by-Step Solution

1
Identify the known and unknown sides of the right triangle formed by the ramp, the ground, and the building.
The hypotenuse (ramp) is c=17c = 17, the horizontal leg (ground) is a=15a = 15, and the vertical leg (height) is bb.
To determine which part of the Pythagorean theorem formula (a2+b2=c2a^2 + b^2 = c^2) needs to be solved.
2
Substitute the known values into the Pythagorean theorem and square them.
152+b2=17215^2 + b^2 = 17^2 becomes 225+b2=289225 + b^2 = 289.
To set up the equation for isolating the unknown variable.
3
Subtract 225 from 289 to isolate b2b^2, then take the square root.
b2=289−225=64b^2 = 289 - 225 = 64. Taking the square root gives b=64=8b = \sqrt{64} = 8.
To find the final linear measurement of the vertical height.

Key Concept

Applying the Pythagorean theorem to find a missing leg of a right triangle.
Estimated Time:45s
Rate this question

Topics

Pythagorean Theorem Word Problems

More questions from this topic