Math Problem Statement

Using the sine rule, calculate the length x. Give your answer to 1 d.p.

Solution

To solve for xx using the sine rule, we can follow these steps:

Given:

  • Angle opposite xx: 4040^\circ
  • Side opposite 5757^\circ: 9cm9 \, \text{cm}

Sine Rule:

xsin(40)=9sin(57)\frac{x}{\sin(40^\circ)} = \frac{9}{\sin(57^\circ)}

Now, we can solve for xx:

x=9×sin(40)sin(57)x = \frac{9 \times \sin(40^\circ)}{\sin(57^\circ)}

Let's calculate that.The length of xx is approximately 6.9cm6.9 \, \text{cm}, rounded to 1 decimal place.

Would you like more details or have any questions?

Here are five related questions to consider:

  1. How is the sine rule applied in different triangle types?
  2. What other methods could solve for xx in this triangle?
  3. How does the sine rule differ from the cosine rule?
  4. Can the sine rule be used for right-angled triangles?
  5. How do you determine when to use the sine rule vs. other trigonometric formulas?

Tip: When using trigonometric rules, ensure your calculator is set to degrees if the angles are provided in degrees!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Rule

Formulas

x = (b * sin(A)) / sin(B)
where A is an angle and b is the length of the side opposite B

Theorems

Law of Sines

Suitable Grade Level

High School