Question

A climbing wall leaning against the top of a play structure forms a right triangle with the ground. The distance from the bottom of the climbing wall to the base of the play structure is 7 feet. If the climbing wall is 11 feet long, how high is the wall of the play structure?

Answer 1

8ft

Explanation:

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Answer 2

The height of wall of play structure is 8.48 feet

Solution:

A climbing wall leaning against the top of a play structure forms a right triangle with the ground

The figure is attached below

ABC is a right angled triangle

AB is the height of wall of play structure

Let "x" be the height of wall of play structure

AB = x

BC is distance from the bottom of the climbing wall to the base of the play structure

BC = 7 feet

AC is the length of climbing wall

AC = 11 feet

We can apply pythogoras theorem for right angled triangle

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

Therefore, by above definition for right angled triangle ABC,

`AC^2 = AB^2+BC^2`

Substituting the values we get,

`11^2 = x^2 + 7^2\\\\121 = x^2 + 49\\\\x^2 = 121-49\\\\x^2 = 72\\\\\text{Take square root on both sides }\\\\x = √(72)\\\\x = 8.48`

Thus the height of wall of play structure is 8.48 feet