I have a basic trig question.?

Question

I need to build a water slide with a slide angle of 65 degrees. I have an 8 foot base. What is the tallest I can make the slide and still have a 65 degree tilt?

Answer 1

a/sin A = b/sin B

Taking the triangle as a right-angled triangle, and letting a be the height and b the base, it works out as:

a/sin 65 = 8/sin 25

a= (8×sin 65)/sin 25 = 17.156 ft

Answer 2

Tangent = Opposite/ Adjacent so

Tan (65 degrees) =  x/8

17.12 feet, i believe.

Answer 3

7.25 ft

The sine of an angle is the opposite side divided by the huypotenuse:  sin = o / a, implying   a sin = o

8 sin(65 degrees) = o = 7.25 ft

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There seems to be some confusion here.  We are all interpreting the question differently.  When you say "8 foot base", what do you mean?

my answer assumes you mean that the slide is 8 feet long, tilted at 65 degrees from horizontal.

If you mean that the 65 degree slide has to fit within 8 horizontal feet, then the 8 tan(65 degrees) = 17.16 feet answer is correct.