Solve Trig Word Problem: Acre Parcel Sides 180 & 240 ft

In summary, to solve a trigonometry word problem involving an acre parcel, you will need to use the trigonometric functions sine, cosine, and tangent to find the angles and sides of the parcel. The Pythagorean theorem can be used to find the length of a missing side in a right triangle in these types of problems. When determining which trigonometric function to use, you should identify the given and unknown measurements and then select the appropriate function. It is possible to use a calculator to solve these problems, but a basic understanding of the concepts and formulas is necessary. Trigonometry word problems have many real-life applications, such as calculating the height of a building or the angle of elevation of a plane.
  • #1
karush
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A one acre parcel has 2 sides 180 ft and 240 ft intersecting at a right angle.
the other side adjacent to the 180 ft is 200 ft what is the length of the 4th side.

by Pythagorean theorem $BD = 300$

so triangle ABD = $21600 \ ft^2$
thus triangle DBC = $21960 \ ft^2$

so 21960 = (1/2)(300)(h) then h=146.4

$$\sqrt{{200}^{2}{}-146.4^2}=136.26$$

$300-136.36 =163.74$

so by Pythagorean theorem $BC$ or the 4th side $\approx$ $219.64 ft$

not sure this is correct, saw another proposed way to do this
using Heron's theorem but after trying it was ?
 
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  • #2
That looks good. I agree with your answer, and I don't see any simpler method for finding it.
 

FAQ: Solve Trig Word Problem: Acre Parcel Sides 180 & 240 ft

1. How do I solve a trigonometry word problem involving an acre parcel with sides measuring 180 and 240 feet?

To solve this problem, you will need to use the trigonometric functions sine, cosine, and tangent. Begin by drawing a diagram of the acre parcel and labeling the given measurements. Then, use the Pythagorean theorem to find the length of the third side. Next, use the appropriate trigonometric function to find the angles of the parcel. Finally, use the Law of Sines or Law of Cosines to find the remaining sides and angles.

2. What is the Pythagorean theorem and how does it relate to solving trigonometry word problems?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In trigonometry word problems, this theorem is often used to find the length of a missing side in a right triangle.

3. How do I determine which trigonometric function to use in a word problem?

The trigonometric functions sine, cosine, and tangent are used to find the ratios of the sides of a right triangle. To determine which function to use, first identify the given measurements and the unknown measurements in the problem. Then, select the appropriate function based on which sides are known and which measurement is being solved for.

4. Can I use a calculator to solve trigonometry word problems?

Yes, a calculator can be used to solve trigonometry word problems. Most scientific calculators have trigonometric functions which can be used to find the values of angles and sides in a right triangle. However, it is important to have a basic understanding of the trigonometric concepts and formulas in order to use the calculator effectively.

5. Are there any real-life applications of solving trigonometry word problems?

Yes, there are many real-life applications of trigonometry word problems. Some examples include using trigonometric functions to calculate the height of a building, the distance between two objects, or the angle of elevation of a plane. Trigonometry is also used in fields such as engineering, surveying, and astronomy.

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