Advanced Trigonometry: Solving for CX in a Triangle with Area 56.4 (3sf)

In summary, the person is trying to find the length of BX in a triangle with known angles and one known length. They are unable to use the cosine rule and are considering using the sine rule to solve the problem.
  • #1
david18
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0
I found the area of this triangle to be 56.4 (to 3sf) easily but i can't work out the length of CX. any ideas?
 

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  • #2
Did you try the cosine law?

c2= a2+ b2- 2ab cos(C)

a= 15, b= 8, and C= 70 degrees.
 
  • #3
sorry i think i worded my question incrorrectly. I'm looking for the length BX. Angle CXB is a right angle. I can't use the cosine rule because i only know one length (15) and one angle (90degrees)
 
  • #4
In other words, x is the point at the foot of the altitude! I was thinking x was th length of AB. You have two right triangles, CXA and CXB. The two given lengths are the lengths of the hypotenuses. Let the two angles at C be a and b. You know that CX/8= sin(a), CX/15= sin(b), and a+ b= 70. Is that enough?
 

FAQ: Advanced Trigonometry: Solving for CX in a Triangle with Area 56.4 (3sf)

What is advanced trigonometry?

Advanced trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles. It involves using trigonometric functions such as sine, cosine, and tangent to solve complex problems involving triangles.

How do I solve for CX in a triangle with area 56.4 (3sf)?

To solve for CX in a triangle with area 56.4, you can use the following formula: CX = √(4A / √3), where A represents the area of the triangle. In this case, A = 56.4, so CX = √(4 * 56.4 / √3) = 13.1 (3 significant figures).

What does the term "3sf" mean in relation to advanced trigonometry?

3sf stands for "3 significant figures". In advanced trigonometry, it is important to round your final answer to the appropriate number of significant figures to maintain accuracy and precision.

What is the importance of solving for CX in a triangle with area 56.4 (3sf)?

Solving for CX in a triangle with area 56.4 (3sf) allows you to determine the length of the missing side of the triangle. This information can be useful in various real-world applications, such as construction, navigation, and surveying.

What other types of problems can be solved using advanced trigonometry?

Advanced trigonometry can be used to solve various problems involving triangles, such as finding missing angles and sides, calculating distances and heights, and analyzing vectors and forces. It is also used in fields such as physics, engineering, and astronomy to solve complex mathematical problems.

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