Pregunta
5. A b-foot ladder touches the side of a
6 .
building at a point 5 feet above the ground.
At what height would a 15 -foot ladder touch
the building if it makes the same angle with
the ground as the shorter ladder?
5. A b-foot ladder touches the side of a | 6 . |
building at a point 5 feet above the ground. | |
At what height would a 15 -foot ladder touch | |
the building if it makes the same angle with | |
the ground as the shorter ladder? |
Ask by Brewer Gibson. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The height at which a 15-foot ladder touches the building is
feet, where
is the length of the shorter ladder.
Solución

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Como
Mind Expander
To determine the height at which the 15-foot ladder will touch the building, we can use the concept of similar triangles since both ladders make the same angle with the ground. The height reached by the first ladder (5 feet) and its length (b feet) gives us a ratio that we can set equal to the ratio for the second ladder (15 feet).
Using the similar triangles relationship:
where
(the height reached by the first ladder) and
is the height reached by the second ladder.
To calculate
(the length of the shorter ladder), we can think of this as a right triangle problem. The relationship can be further simplified to:
If we assume
is a constant in relation to
, let’s say
, then with
, we can calculate the combined ratios and eventually find
. Solving that gives you a similar height based on the properties of the triangles. If you need specific numbers, we can assign values and find exact ratios.
In the previous relation,
which simplifies our task. If we want numerical specifics, more information about
is needed to finalize the answer!

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