Can anyone walk me through these trigonometry questions?

1) A surveyor measures the top of a building 50 ft away from him. His angle-measuring device is 4 ft above ground. The angle of elevation to the top of the building is 63 degrees. How tall is the building?

2) An airplane pilot can see the top of a traffic control tower at a 20 degree angle of depression. The airplane is 5,000 ft from the tower. What is the altitude of the plane?

3) A forest ranger looking out from a ranger's station can see a forest fire at a 35 degree angle of depression. The ranger's position is 100 ft above the ground. How far is it from the ranger's station to the fire?

6 answers

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ANSWER #1 of 6

1. So you have the angle of elevation 63 degrees, you also have the distance of the person from the building, which is 50 ft. From that information, you must decide whether to use sine, cosine, or tangent.
Imagine, or draw the triangle. If you draw the triangle right, you should have 50 ft as the adjacent, with your degree of 63 and the side you are trying to find should be the opposite. This should be an indication that you are to use tangent. And since you have the angle, you use Tangent instead of arcTan.
Tangent = opposite/adjacent
so you have tan63= X/50
tan63x50 = X
1.96 x 50 = 98.13 ft Now remember the device is 4 ft above ground so add 4 ft to that and you get 102.13

2. Again draw your triangle. You should have the angle as 20 degress, and the adjacent is 5000ft, and the side you are looking for is the opposite. Again you use tangent because you have the adjacent and are looking for the opposite.
tan20=opposite/5000
tan20 x 5000= opposite
1819.85 ft is your opposite or your altitude from the tower.

3. 100ft should be your opposite, and you are looking for the adjacent.
tan 35=1000/adjacent adjacent=1428 So it is 1428 feet from the fire.


ANSWER #2 of 6

Thank you so much! Not good at this trig stuff at all, but this made a lot of sense!

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ANSWER #3 of 6

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ANSWER #4 of 6

My suggestion is to sketch out the scenario described in word problems. Once you have a sketch you can find the right triangles, ratios between sides, etc.

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ANSWER #5 of 6

Yeah, my teacher always says, "When in doubt, draw it out."

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ANSWER #6 of 6

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