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Area of Triangle Game (Sine)
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This Area of Triangle Game (Sine) is a great way to put your skills to the test in a fun environment. By practicing, you’ll start to work out the answers efficiently.
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Area of Triangle Game (Sine)
The standard formula for the area of a triangle is \(\text{Area} = \frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height. However, when you don’t know the height (\(h\)), you can use the sine of an angle to find the area, provided you know two sides and the angle between them (SAS). The formula is \(\text{Area} = \frac{1}{2}ab \sin(C)\). Scroll down the page for a more detailed explanation.
In this game, you may select “Find Area”, “Find Side, “Find Angle” or “Mixed Challenge”. Solve the given problem and select one of the answers. The game includes a scoring system, and clear feedback to help you master this skill.
Triangle Area Master
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How to Play the Area of Triangle Game (Sine)
This game helps you practice using the sine function to calculate the area of a non-right-angled (oblique) triangle. It has four modes: “Find Area”, “Find Side, “Find Angle” or “Mixed Challenge”.
Here’s how to play:
- Select Game Mode: Select “Find Area”, “Find Side, “Find Angle” or “Mixed Challenge”.
- Find Area: You will be given two sides and the included angle. Find the area of the triangle.
- Find Side: You will be given the area of a triangle, a side and an angle. Find the missing side of the triangle.
- Find Angle: You will be given the area of a triangle, and two sides. Find the missing included angle.
- Select Your Answer: Calculate and select you answer.br>
- Check Your Work: The game will tell you if you’re correct. If you are wrong, the correct answer will be highlighted in green.
- Get a New Problem: Click “Next Problem” for a new problem.
Your score is tracked, showing how many you’ve gotten right. - Finish Game When you have completed 10 questions, the game will give you your final score.
Find the Area of a Triangle using the Sine Function
The standard formula for the area of a triangle is \(\text{Area} = \frac{1}{2}bh\), where \(b\) is the base and \(h\) is the height. However, when you don’t know the height (\(h\)), you can use the sine of an angle to find the area, provided you know two sides and the angle between them (SAS). This is often called the SAS Area Formula (Side-Angle-Side Area) or the Trigonometric Area Formula.
The Trigonometric Area Formula
For any triangle with sides \(a\), \(b\), and \(c\), and opposite angles \(A\), \(B\), and \(C\), the area is given by one of the following formulas:
\(\text{Area} = \frac{1}{2}bc \sin(A)\)
\(\text{Area} = \frac{1}{2}ac \sin(B)\)
\(\text{Area} = \frac{1}{2}ab \sin(C)\)
Step-by-Step Example
Find the area of a triangle where:
Side \(b = 12\) cm
Side \(c = 9\) cm
The included angle \(A = 62^\circ\)
Step-by-Step Solution:
Identify the known information (SAS):
Side \(b = 12\)
Side \(c = 9\)
Included Angle \(A = 62^\circ\)
Choose the correct formula: Since we know \(b\), \(c\), and \(A\), we use the formula:
\(\text{Area} = \frac{1}{2}bc \sin(A)\)
Substitute the values:
\(\text{Area} = \frac{1}{2}(12)(9) \sin(62^\circ)\)
Calculate the product of the sides:
\(\text{Area} = \frac{1}{2}(108) \sin(62^\circ)\)
\(\text{Area} = 54 \sin(62^\circ)\)
Find the sine value:
\(\sin(62^\circ) \approx 0.8829\)
Calculate the final area:
\(\text{Area} \approx 54 \cdot (0.8829)\)
\(\text{Area} \approx 47.68\)
The area of the triangle is approximately \(\mathbf{47.68}\) square centimeters.
The video gives a clear, step-by-step approach to calculate the area of a triangle using the sine function.
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