Question

Urgent help!!

Find ABC pls

(Grade 9 math btw)

Answer 1

A = x√3

B = 2x

C = x

Explanation:

Find the values of the side lengths, A, B, and C of the given triangle.

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To find the side lengths of a triangle when only the angles are given, you would need additional information such as the length of at least one side or the radius of the circumscribed or inscribed circle.

In a triangle, the side lengths are determined by the interplay between angles and side lengths, as defined by trigonometric functions (sine, cosine, and tangent). Without any information regarding the side lengths, it is not possible to determine them solely based on the angles.

However, this is a special right triangle. Specifically, a 30-60-90 triangle.
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In a 30-60-90 triangle, the side lengths are in a specific ratio of 1:√3:2.

If we consider the shortest side (opposite the 30-degree angle) to have a length of "x," then the other two sides can be determined as follows:

• The side opposite the 60-degree angle will have a length of x multiplied by the square root of 3 (√3).

• The hypotenuse (opposite the 90-degree angle) will have a length of 2x.

So, the side lengths of a 30-60-90 triangle can be expressed as:

Shortest side (opposite 30-degree angle) = x

Side opposite 60-degree angle = x√3

Hypotenuse (opposite 90-degree angle) = 2x

These ratios hold true regardless of the actual measurements of x, as long as the ratios remain consistent.
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Additional Info:

What is a special right triangle?

A special right triangle is a triangle that has some unique properties and relationships between its angles and side lengths. These triangles are special because their side lengths can be expressed as simple ratios and their angles have specific, consistent values.

There are two types of special right triangles: the 45-45-90 triangle and the 30-60-90 triangle.