Math Problem Statement

Calculate the length of p. Give your answer in millimetres to 1 d.p.

Solution

To solve for pp, we can use the law of sines since we have a non-right-angled triangle and know two angles (67° and 38°) and one side (16.5 mm). Here's how:

  1. Sum of angles in a triangle: The third angle in the triangle can be calculated as: 1806738=75180^\circ - 67^\circ - 38^\circ = 75^\circ So, the third angle is 75°.

  2. Using the Law of Sines: The law of sines states: psin(38)=16.5 mmsin(75)\frac{p}{\sin(38^\circ)} = \frac{16.5 \text{ mm}}{\sin(75^\circ)}

  3. Solving for pp: p=16.5×sin(38)sin(75)p = \frac{16.5 \times \sin(38^\circ)}{\sin(75^\circ)}

Let's calculate this now.The length of pp is approximately 10.5 mm, rounded to one decimal place.

Would you like further details on the solution or any clarifications?

Here are some related questions you might want to explore:

  1. How can you use the Law of Cosines in solving triangle problems?
  2. What is the significance of the Law of Sines in non-right-angled triangles?
  3. How do we calculate angles in a triangle given two sides and an angle?
  4. Can we solve similar problems using trigonometric identities?
  5. How can you determine whether a triangle is obtuse, acute, or right-angled based on its angles?

Tip: Always ensure that your calculator is in the correct mode (degrees or radians) when working with trigonometric functions.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Law of Sines
Angle Sum in a Triangle

Formulas

Law of Sines: sin(A)/a = sin(B)/b
Angle sum in a triangle: A + B + C = 180°

Theorems

Law of Sines

Suitable Grade Level

Grades 10-12