TRIG PLZ HELP An escalator at a shopping center is 200 ft
9 in. long, and rises at an angle of 15 What is the vertical rise of the escalator? Round to the nearest inch.
.
10. A straight ramp rises at an angle of 25.5 and has a base 30 ft long. How high is the ramp? Round to the nearest foot.

Question

TRIG PLZ HELP An escalator at a shopping center is 200 ft 
9 in. long, and rises at an angle of 15 What is the vertical rise of the escalator? Round to the nearest inch.
.
10. A straight ramp rises at an angle of 25.5 and has a base 30 ft long. How high is   the ramp? Round to the nearest foot.

SmokeyBrown · Answer

Hi and welcome to QuestionCove!

As you can hopefully see from my crudely-drawn diagrams, both questions can be solved by taking a trigonometric property of the right triangles using the information given and then calculating the unknown value.

In the escalator example, we are given the hypotenuse length as 200.75 ft (200 ft and 9 inches) and the angle of 15 degrees and need to solve for the height, which is the length opposite the angle. The height over the hypotenuse is also the SINE of the triangle, so we can calculate
sin(15) = h/200.75 in order to solve for h

Similarly, in the ramp example, we are given the base as 30 ft and the angle of 25.5 degrees and need to solve for the height. The height over the base is also the TANGENT of the triangle, so we can calculate tan(25.5) = h/30 in order to solve for h

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