### Trig Ratios 30 60 90

Example No. 2 We can tell that this is a 30-60-90 triangle since it is a right triangle with one specific dimension, 30. The unmarked angle must thus be 60 degrees. Because 18 is the measure opposite the 60 degree angle, it must equal $x3$. The shortest leg must therefore be $18/3$ in length. (Because a denominator cannot include a radical/square root, the leg length will be $18/33 * 3/33 = 183/3 = 63$.) And the hypotenuse will be $2(18/3)$ (Remember that a radical cannot be in the denominator, thus the final result will be 2 times the leg length of $63$ => $123$).

So, if we saw a right triangle with a second angle of 30, we'd know that the third missing angle is 60.

We can also use the first characteristic given above to calculate the angles of a right triangle since it always has one 90-degree angle. The other two angles must sum up to 90 to complete the triangle's 180, therefore none of the other two angles may be greater than 90.

To get the length of the hypotenuse, c, multiply the shorter leg by 2 to get eq6sqrt3 /eq

To reach the right place on the wall, the ladder must be extended eq6sqrt3/eq feet. The distance between the bottom of the wall and where the ladder meets the wall is eq3sqrt3/eq.

Related Topics:Examples, answers, and videos to assist GCSE Math students in learning how to calculate Trig Ratios for multiples of 30, 45, and 60 degrees.

The graphic below depicts the trig ratios of the following special angles: 0, 30, 45, 60, and 90. More examples and solutions for trigonometric ratios may be found further down the page. Trigonometry - 30 and 60 degree trigonometric ratios In this lesson, I will demonstrate how to compute the precise values of sin, cos, and tan at 30 and 60 degrees. Trigonometry - 45 degree trigonometric ratios In this lesson, I will demonstrate how to compute the precise values of sin, cos, and tan of 45 degrees. Positive multiples of 30, 45, and 60 degrees have trigonometric ratios. In this video, I'll teach you how to compute sin, cos, and tan for positive multiples of 30 and 60 degrees. Negative multiples of 30, 45, and 60 degrees have trigonometric ratios. In this article, I'll teach you how to compute sin, cos, and tan for negative multiples of 30 and 60 degrees.

### Trigonometric Ratios 30-60-90 Triangle

In the 30-60-90 triangle ABC depicted below, N = 30, R = 60, and M = 90. The definitions below help us understand the relationship between the two sides: Because 30 is the lowest angle in this triangle, the side opposing 30 will always be the smallest, RM = x.

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