Question

In the scenarios you have explored so far, the angle measures were given, and you used trigonometric ratios to find missing side lengths. To determine the angle measures when only the side lengths are given, you can use inverse trigonometric functions. The input of each function is a number, which represents a ratio of two of the sides. The output of each function is an acute angle measure.Inverse sine: If sin A = z is given, then angle A can be determined by sin ¹2 = A.Inverse cosine: If cos A = x, is given, then angle A can be determined by cos ¹ = A.Inverse tangent: If tan A = z, is given, then angle A can be determined by tan ¹ = A.Let's explore this idea using the familiar 45°-45°-90° isosceles right triangle.

Answer 1

Given:-

A right angled triangle with side length 1.

To find the required angle value.

So now we use different trigonometric ratios such as,

`sin,cos,tan`

So we get,

`sin^(-1)((1)/(√(2)))=cos^(-1)((1)/(√(2)))=tan^(-1)((1)/(1))=45`

So the required angle is 45 degree.