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Give the definition of similar triangle?
Similar triangles means they have the same lengths OR the corresponding lengths have equal ratios.
Do corresponding sides of similar triangles have the same measure?
No, corresponding sides of similar triangles do not have the same measure; instead, they are proportional. This means that while the lengths of the corresponding sides differ, the ratios of their lengths remain constant. For example, if one triangle has sides of lengths 3, 4, and 5, and a similar triangle has sides of lengths 6, 8, and 10, the corresponding sides maintain the same ratio (2:1).
What would be a situation in which the lengths of two sides of a right triangle are known but the measure of an angle is needed?
In a right triangle where the lengths of two sides are known, such as the lengths of one leg and the hypotenuse, you can use trigonometric ratios to find the measure of an angle. For example, if you know the lengths of the opposite side and the hypotenuse, you can use the sine function: (\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}). By taking the inverse sine (arcsin) of the ratio, you can calculate the angle (\theta). Similarly, you can use cosine or tangent depending on which sides you have.
What calculation is different in finding missing side lengths and angle measures in a right triangle using the trigonometric functions?
When finding missing side lengths in a right triangle using trigonometric functions, you typically apply ratios like sine, cosine, or tangent, which relate the angles to the lengths of the sides. Conversely, when calculating missing angle measures, you use the inverse trigonometric functions (such as arcsine, arccosine, or arctangent), which take the ratios of the sides and return the corresponding angles. Thus, the key difference lies in using direct ratios for side lengths and inverse functions for angles.
Do the corresponding sides of similar triangles have proportional lengths?
Yes, the corresponding sides of similar triangles have proportional lengths. This means that the ratios of the lengths of corresponding sides are equal. For example, if two triangles are similar, the ratio of the lengths of one triangle's sides to the lengths of the other triangle's corresponding sides will be the same across all three pairs of sides. This property is fundamental in solving problems related to similar triangles.
Give the definition of similar triangle?
Similar triangles means they have the same lengths OR the corresponding lengths have equal ratios.
How can you use ratios of the side lengths to find the angle measures of the acute angles in a right triangle?
By using trigonometry that is applicable to a right angle triangle.
What is the ratios function of sin?
The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.In terms of ratios, the sine of an angle is defined, in a right angled triangle, as the ratio of lengths of the opposite side to the hypotenuse.
What would be a situation in which the lengths of two sides of a right triangle are known but the measure of an angle is needed?
In a right triangle where the lengths of two sides are known, such as the lengths of one leg and the hypotenuse, you can use trigonometric ratios to find the measure of an angle. For example, if you know the lengths of the opposite side and the hypotenuse, you can use the sine function: (\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}). By taking the inverse sine (arcsin) of the ratio, you can calculate the angle (\theta). Similarly, you can use cosine or tangent depending on which sides you have.
What calculation is different in finding missing side lengths and angle measures in a right triangle using the trigonometric functions?
When finding missing side lengths in a right triangle using trigonometric functions, you typically apply ratios like sine, cosine, or tangent, which relate the angles to the lengths of the sides. Conversely, when calculating missing angle measures, you use the inverse trigonometric functions (such as arcsine, arccosine, or arctangent), which take the ratios of the sides and return the corresponding angles. Thus, the key difference lies in using direct ratios for side lengths and inverse functions for angles.
Why do trigonometric ratios do not depend on the size of the right triangle?
Because a right angle will always measure 90 degrees no matter what the dimensions of the triangle are.
Do the corresponding sides of similar triangles have proportional lengths?
Yes, the corresponding sides of similar triangles have proportional lengths. This means that the ratios of the lengths of corresponding sides are equal. For example, if two triangles are similar, the ratio of the lengths of one triangle's sides to the lengths of the other triangle's corresponding sides will be the same across all three pairs of sides. This property is fundamental in solving problems related to similar triangles.
What are the 3 basic trig ratios and how do they work?
The three basic ratios are sine, cosine and tangent.In a right angled triangle,the sine of an angle is the ratio of the lengths of the side opposite the angle and the hypotenuse;the cosine of an angle is the ratio of the lengths of the side adjacent to the angle and the hypotenuse;the tangent of an angle is the ratio of the lengths of the side opposite the angle and the the side adjacent to the angle.
How do ratios of side lengths compare for similar triangles?
they both have the same ratios
Is a triangle with sides 60 80 and 100 a right triangle?
Yup, it follows the 3, 4, 5 rule (or in this case 6, 8, 10). Triangles with those ratios in the lengths of its sides are always right triangles
What does trigonometric ratios mean?
They may be defined as the ratios of the lengths of sides of a right angled triangle, relative to either of the other angles.sine = opposite/hypotenusecosine = adjacent/hypotenusetangent = opposite/adjacentcosecant = hypotenuse/oppositesecant = hypotenuse/adjacentcotangent = adjacent/opposite.
What two ratios measure factors that affect profitability?
what tw ratios measure factors
