• angle functions
• trigonometric function graph
• complex numbers

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Dear Professor Cram:

An escalator is 152 feet in length rises to a platform and makes a 30 degree angle with ground. Find the height of the platform using a trigonometry equation.

Ekta, Middlesex Community College

Thanks for your question, Ekta.

The problem you describe is a classic sine function equation. Imagine the platform at the top of a right triangle, with the right angle lying directly beneath it and the escalator running up the hypotenuse. The 30° angle is formed between the foot of the escalator and the ground, and the height of the platform is the side opposite the angle.

The equation for finding the sine of an angle is:

sin A = opposite/hypotenuse

If you multiply both sides of this equation by the hypotenuse, you solve for the opposite side:

opposite = (sin A)(hypotenuse)

Now, let's substitute the values into our equation to find the answer:

opposite = (sin 30°)(152 feet)

opposite = (0.5)(152 feet)

opposite = 76 feet

I hope this helps. Let us know if you need anything else.