# Area of Triangle Using Trigonometry Worksheets

For several years, by now, you have known how to calculate the area of a triangle. We want to show you another way to perform this same analysis. There are a wide number of application where this makes more sense and may provide you with a more precise final solution. There will also be situations where you do not have the ability to measure the height of a triangle. This could be logistical because you simply do not have the ability to get in there an actually take the measurement. In those cases, using this type of math can move you along much quicker. It is always a good idea to understand multiple ways to achieve something. What an awesome selection of worksheets and lessons to allow students to learn how to use trig. to solve problems that involve finding the areas of triangles.

### Aligned Standard: HSG-SRT.D.9

- Express the Area Step-by-Step Lesson- You are given the length of a leg, the hypotenuse, and the measure of one angle. Now go get the area!
- Guided Lesson - These are some really unique triangles. I promise!
- Guided Lesson Explanation - What a way to answer these. I it a bit boiler plate, but that's what they want on this skill.
- Practice Worksheet - I tried to add a bit more thought into these problems and it does show pretty well.
- Matching Worksheet - Match the measures to the problems. I am a bit embarrassed that I didn't use units on a single one.
- Area of Triangle Using Trigonometry Worksheet Five Pack - I describe a ton of triangles and you will find the area or use it to your advantage.
- Triangle Problems Worksheet Five Pack - These types of problems make some students uncomfortable.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

I still remember the first day I saw this skill. It was so powerful!

- Homework 1 - Express the area rounded to three decimal places.
- Homework 2 - In an isosceles triangle, the two equal sides each measure 5 meters, and they include an angle of 85°. Find the area of the isosceles triangle, to the nearest square meter.
- Homework 3 - In Triangle PQR, PQ = 8, PR = 4, and m

### Practice Worksheets

The practice sheets give you a good balance of questions to work with.

- Practice 1 - In Δ UVW, UV = 7, UW = 18, and m < U = 34°. Find the area of Δ UVW, to the nearest tenth of a square unit.
- Practice 2 - Why would you positon a triangle to the right, when it could go left?
- Practice 3 - In a rhombus, each side is 24, and one angle is 175°. Find the area of the rhombus, to the nearest square unit.

### Math Skill Quizzes

The last quiz seems to be the most difficult for kids.

- Quiz 1 - In triangle PQR, PQ = 30 meters and PR = 21 meters. If the area of the triangle is 210 sq. meters, find the measure of < P to the nearest degree.
- Quiz 2 - Using Heron's formula, find the area of the triangle, to the nearest tenth.
- Quiz 3 - In an isosceles triangle, the two equal sides each measure 25 meters, and they include an angle of 55°. Find the area of the isosceles triangle, to the nearest sq. meter.

### How to Determine the Area of a Triangle Using Trigonometry

We all know the general formula for calculating the area of a triangle. It is expressed as: A= 1/2 b x h. In the above formula, 'b' is defined as the base or length of a side, where 'h' is defined as the height draw to the side. Reading from the above formula, we say that the area of the triangle is half the length of one side times the height drawn with it.

This method that we are accustomed to using is based on algebra. However, there is another way to measure the area of a triangle. Trigonometry is not only used to find different angles and sides of a right-angled triangle; we use trigonometry to calculate the area of a triangle. Using the above right-angled triangle, we can say, sin C = h/b. Multiplying the above equation by b, we get: b sin C = h. The height of the triangle can now be written as b sin C. Replacing this new value of height in the general formula for calculating the area of a triangle. A= 1/2 ab sin C. Where the letters 'a' and 'b' express any two sides of the triangle, and C represents the included angle. With this derived formula, we aren't required to find the height of the triangle. If you know the two sides and their included angle, you can substitute these values in this formula to find the area of the triangle.

Based on the knowledge of a system you are presented with, there will be times where one of these two methods from determining the area of a triangle is more advantageous to use then the other. The trigonometric method is often more helpful in situations where a great deal of precision is required. It is often the preferred method in many forms of manufacturing and design situations.