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Answer:
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.
where <em>a</em> and<em> b</em> are the legs and <em>c</em> is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:
- a= 9 cm
- b= 11 cm
Substitute these values into the formula.
Solve the exponents.
- (9 cm)²= 9 cm*9 cm=81 cm²
- (11 cm)²= 11 cm*11 cm= 121 cm²
Add the values on the left side.
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
We are told to round to the nearest tenth.
- 14.2<u>1</u>26704036
The 1 in the hundredth place tells us to leave the 2 in the tenth place.
The hypotenuse is equal to <u>14.2 centimeters.</u>
Answer:
Step-by-step explanation:
The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.
For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared (), where
is the hypotenuse.
Let the length of the ladder be (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as
.
From the Pythagorean Theorem, we then have:
Expand using :
Subtract from both sides and add
to both sides:
Combine like terms:
Divide both sides by 2:
Therefore, the length of the ladder is 25 feet.