Question

For a right triangle ABC, you are told that cos A = x and sin A = y. Which option below gives an expression that is
equivalent to tan A?
OX

Answer 1

Equivalent to tan A =$\frac{y}{x}$

What is meant by the right triangle?

• A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The sum of the other two angles is 90 degrees. The perpendicular and the triangle's base are the sides that make up the right angle. The third side is the longest of the three sides, known as the hypotenuse.
• A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilize specific terminology.
• A right triangle is a triangle in which one of the angles is at a right angle or two of the sides are perpendicular, or more formally, an orthogonal triangle, formerly known as a rectangled triangle.

Equivalent to tan A:

A right triangle ABC so that m∠C = 90°

The lengths are:

                           Side a is opposite ∠A,

                           Side b is opposite ∠B,

                           Side c (the hypotenuse) is opposite ∠C

Because cos A = x, therefore

$x =\frac{b}{c}$  => $b = cx$                  (1)

Because sin A = y, therefore

$y =\frac{a}{c}$ => $a = cy$                 (2)

By definition,

tan A = a/b

         $=\frac{cy}{cx}$

        $=\frac{y}{x}$

Equivalent to tan A =$\frac{y}{x}$

To learn more about the right triangle, refer to:

https://brainly.com/question/2217700

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