Question

The sine and cosine of one of the acute angles in a right triangle are equal. What is the tangent of the angle?

Answer 1

Answer:

1

Step-by-step explanation:

Since tan(x) = sin(x)/cos(x), if sin(x) = cos(x) then tan(x) must be 1.

You can even reason that the acute angle is 45° and sin(x)=cos(x) = $\frac12\sqrt2$.

Answer 2

The tangent of the angle is equal to 1.

Given

The sine and cosine of one of the acute angles in a right triangle are equal.

Tangent of the angle;

The tangent of the angle is defined as the ratio of perpendicular or base of the right-angle triangle.

The sine, cosine, and tangent of an acute angle of a right-angled triangle are defined as the ratio of two of three sides of the right-angled triangle.

The tangent angle can be represented as;

$\rm Tan \theta=\dfrac{Sin\theta}{Cos\theta}$

The sine and cosine of one of the acute angles in a right triangle are equal.

$\rm Sin\theta=Cos\theta$

Therefore,

The tangent of the angle is;

$\rm Tan \theta=\dfrac{Sin\theta}{Cos\theta}\\\\\rm Tan \theta=\dfrac{Cos\theta}{Cos\theta}\\\\\rm Tan \theta=1$

Hence, the tangent of the angle is equal to 1.

To know more about trigonometric ratios click the link given below.

https://brainly.com/question/1578568