Question

1.) The trig ratio needed to solve the problem and how that it is the correct trig function.

2.) A step-by-step solution rounded to the nearest tenth
P.s The bottom number is 100ft

Answer 1

In every right triangle, you have the following identites:

`o = h\sin(\alpha),\quad a = h\cos(\alpha)`

Where
`\alpha` is one of the acute angles,
`o` is the leg opposite to the angle,
`a` is the leg adjacent to the angle and
`a` is the hypothenuse.

In this case, we know that the adjacent leg is 100ft long, so we can use the second formula to compute the hypothenuse:

`100 = h\cos(37) \implies h = (100)/(\cos(37))`

Now let's use the first equation to compute the length of the opposite leg, i.e. the one you're interested in:

`o = h\sin(\alpha) = (100)/(\cos(37))\sin(37)`

Note that the ratio between the sine and the cosine is the tangent:

`o = 100\tan(37)`

If you ask for the tangent of 37 to a calculator, you get

`\tan(37) \approx 0.753554050\ldots`

So, you have

`100\tan(37) \approx 75.3554050\ldots`

Which rounded to the nearest tenth is 75.36