Abuilding is 50 ft high. at a distance away from the building, a person notices that the angle of elevation with the ground to the top of the building is 41°. how far is the person from the base of the building?

My go-to first step - draw a diagram! This way we can easily see what values we have and what we need to work out.

Next, label each side of the triangle as either the hypotenuse, adjacent, or opposite. I like to subtly abreviate those to H, A, and O, respectively.

Now take a look at our SOH CAH TOA. We have the value of the opposite side, and we need the value of the adjacent side, so look for the one with both opposite and Adjacent. TOA meets this criteria.

This bit is the bit that often trips people up. To avoid too much confusion, rewrite TOA in a wee magic triangle as shown in the image. We want to find the adjacent, so we cover up adjacent, and are left with O ÷ T. This provides the basic skeleton for our equation.

Substitute in 50 for O, and divide that by the tan of the angle (tan41). The answer is that the person is 57.5 feet away from the building. Don't forget units ;)

If you got some weird result like 311.2 or something strange, double check your calculator, as it may be on radians setting instead of degrees setting, which will cause all sorts of chaos when trying to do trigonometry.

Hope I helped :D

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