Trig problem

[Darya]

Determine the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. The result must be in centimeters.

So we have a right triangle here. I expected 29,6*18 to be a hypotenuse, then it's sinus function. What am I doing wrong?
Thank you!

 

[Cubist]

By "length of step" they probably mean the horizontal length - the length that is stood on (below the hypotenuse in your pic).

FYI: I just looked up online and I think the proper term for this length is the "run" (and the height of the step is called the "rise").

 

[Tavasanis]

I understand that the length of every step represents the base of the triangle. Therefore, [MATH]\tan 30º=\dfrac{h}{28.6}[/MATH], where [MATH]h[/MATH] is the height of every step. The total height should then be [MATH]\tan 30º \times 28.6 \times 18=\dfrac{1}{\sqrt{3}}\times 28.6 \times 18 = 297.22[/MATH] cm.

 

[Darya]

By "length of step" they probably mean the horizontal length - the length that is stood on (below the hypotenuse in your pic).

FYI: I just looked up online and I think the proper term for this length is the "run" (and the height of the step is called the "rise").

Yes, it's correct, because if I plug in tan function I get the right answer. It's weird though. I still dont get the logic

 

[Cubist]

The question author was probably trying to teach the use of trigonometry within an applied, real world, context. This can help people to use their knowledge of trig when they encounter a real-world problem in later life.

But they should really use the correct terms for the lengths OR they should supply a diagram to illustrate their intention!

If you encounter a question like this in an exam, and you're not sure what length the question is talking about, then clearly write "I assume the step length is referring to the <hypotenuse, horizontal distance, whatever>". Then you should still obtain most of the available marks.

 

[Darya]

The question author was probably trying to teach the use of trigonometry within an applied, real world, context. This can help people to use their knowledge of trig when they encounter a real-world problem in later life.

But they should really use the correct terms for the lengths OR they should supply a diagram to illustrate their intention!

If you encounter a question like this in an exam, and you're not sure what length the question is talking about, then clearly write "I assume the step length is referring to the <hypotenuse, horizontal distance, whatever>". Then you should still obtain most of the available marks.

thank you for a great tip! have a nice day!!