30-15 Related: Chapter 6 - The Triangles and its properties, Mathematics, Class 7 (VII)

Question

30-15 Related:  Chapter 6 - The Triangles and its properties, Mathematics, Class 7 (VII)

Answer

Chapter 6 - The Triangles and its properties

30-15 Related

In the study of triangles, the 30-15-90 triangle and the 45-45-90 triangle are two important right triangles.

30-15-90 Triangle

A 30-15-90 triangle is a right triangle in which one angle measures 30 degrees and another angle measures 15 degrees.

The third angle must be 90 degrees, making it a right triangle.

The sides of a 30-15-90 triangle are in a specific ratio. The hypotenuse is twice the shorter leg, and the longer leg is the square root of three times the shorter leg.

The ratio of the sides is 1:√3:2

Example: If the shorter leg is 6, then the longer leg is 6√3 and the hypotenuse is 12.

45-45-90 Triangle

A 45-45-90 triangle is a right triangle in which both acute angles measure 45 degrees.

The third angle must be 90 degrees, making it a right triangle.

The sides of a 45-45-90 triangle are also in a specific ratio. The two legs are congruent and the hypotenuse is the square root of two times one of the legs.

The ratio of the sides is 1:1:√2

Example: If one leg is 5, then the other leg is also 5 and the hypotenuse is 5√2.

These two triangles are important in geometry because they appear in many real-world situations. Knowing the properties and ratios of these triangles can help solve problems involving angles, sides, and distances.

Answer

15

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