Question

A, B & C form the vertices of a triangle.

∠
CAB = 90°,
∠
ABC = 58° and AB = 9.3.
Calculate the length of BC rounded to 3 SF.

Answer 1

To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.

Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.

Using the sine function, we can find the length of BC:

sin(∠BCA) = BC / AB

Rearranging the formula, we have:

BC = AB * sin(∠BCA)

Substituting the given values:

BC = 9.3 * sin(32°)

Using a calculator or trigonometric table, we find:

BC ≈ 9.3 * 0.529 = 4.917

Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.

Explanation: