What is the ratio of the sides of a right triangle?

The sides in this triangle are in the ratio 1 : 1 : √2, which follows immediately from the Pythagorean theorem. Of all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely √22.

How can the concept of trigonometric ratios be applied in real life situation?

Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings etc. It is used naval and aviation industries. It is used in cartography (creation of maps).

Why are the trigonometric ratios the same for all 30 60 90 triangles?

The shortest and longest sides in any triangle are always opposite to the smallest and largest angles. Triangles with the same angle measures are similar, and their sides will always be in the same ratio to each other. The concept of similarity can therefore be used to solve problems involving the 30-60-90 triangles.

What is the importance of solving the six trigonometric ratios?

The six main trigonometric functions are sine, cosine, tangent, secant, cosecant, and cotangent. They are useful for finding heights and distances, and have practical applications in many fields including architecture, surveying, and engineering.

What are some real life applications of trigonometry?

Other Uses of Trigonometry

• The calculus is based on trigonometry and algebra.
• The fundamental trigonometric functions like sine and cosine are used to describe the sound and light waves.
• Trigonometry is used in oceanography to calculate heights of waves and tides in oceans.
• It used in the creation of maps.

What is the relationship between the sides of a 30-60-90 triangle?

Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).

What is the main trigonometric ratio between the opposite side and adjacent side of a right triangle?

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.