Question

Using the inverse of sine, cosine and tangent allow us to find A missing side in a right triangle A missing angle in a right triangle The perimeter of a right triangle Triangular area

Answer 1

Answer:

A missing angle in a right angle.

Step-by-step explanation:

Given, the inverse of trigonometric functions sine, cosine and tangent.

To find:

The value that can be found using the inverse trigonometric functions.

Solution:

First of all, let us consider the right angled triangle attached in answer area.

Hypotenuse is AC, Base is BC and AB is the Altitude/Height of the right angled $\triangle ABC$.

Let us suppose all three sides are known and $\angle C$ is unknown.

Formula:

$1.\ sin\theta = \dfrac{Perpendicular}{Hypotenuse}$

$2.\ cos\theta = \dfrac{Base}{Hypotenuse}$

$3.\ tan\theta = \dfrac{Perpendicular}{Base}$

Let us consider $\angle C$.

$sin C = \dfrac{AB}{BC}$

If we taken inverse:

$sin^{-1} sinC = sin^{-1} (\frac{AB}{BC})$

$\Rightarrow \angle C = sin^1\frac{AB}{BC}$

Similar is the case for cosine and tangent.

Therefore, the missing angle of the right angled triangle can be calculated by the inverse of sine, cosine and tangent.