Question

A street slopes upward at an angle of 15o with the horizontal. How high does it rise over a horizontal distance of 120 meters? Explain the thinking you use to arrive at your answer.

Answer 1

Answer: $32.15\ meters$

Step-by-step explanation:

You can draw a right triangle (Observe the figure attached. It is not drawn to scale), where "x" is the the amount of meters the street rises over a horizontal distance of 120 meters.

You need to use the following Trigonometric Identity:

$tan\alpha=\frac{opposite}{adjacent}$

In this case, you can identify that:

$\alpha=15\°\\\\opposite=x\\\\adjacent=120$

Then, knowing these values, you can substitute them into$tan\alpha=\frac{opposite}{adjacent}$:

$tan(15\°)=\frac{x}{120}$

And finally, you must solve for "x" in order to find its value.

You get this result:

$(tan(15\°)(120)=x\\\\x=32.15$