Concept explainers
a.
To calculate: The ratio of sine of
a.
Answer to Problem 2PSA
The ratio of sine of
Explanation of Solution
Given information:
A
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC.
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
To find
We know that,
Therefore,
b.
To find: A ratio formed by cosine of
b.
Answer to Problem 2PSA
The ratioformed by cosine of
Explanation of Solution
Given information:
A triangle with angles as
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC .
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
By Pythagoras theorem,
To find
We know that,
Therefore,
c.
To calculate: A ratio formed by tangent of
c.
Answer to Problem 2PSA
The ratio formed by tangent of
Explanation of Solution
Given information:
A triangle with angles as
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC .
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
By Pythagoras theorem,
To find
We know that,
Therefore,
d.
To find: A ratio formed by sine of
d.
Answer to Problem 2PSA
The ratio formed by sine of
Explanation of Solution
Given information:
A triangle with angles as
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC .
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
By Pythagoras theorem,
To find
We know that,
Therefore,
e.
To calculate: A ratio formed by cosine of
e.
Answer to Problem 2PSA
The ratio formed by cosine of
Explanation of Solution
Given information:
A triangle with angles as
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC .
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
By Pythagoras theorem,
To find
We know that,
Therefore,
f.
To calculate: A ratioformed by tangent of
f.
Answer to Problem 2PSA
The ratioformed by tangent of
Explanation of Solution
Given information:
A triangle with angles as
As sum of angles in a triangle is
Formula used:
Calculation:
Consider an equilateral triangle ABC .
Since each angle is an equilateral triangle is
Draw the perpendicular line AD from A to the side BC.
Now,
Therefore BD=DC and also
Now observe that the triangle ABD is a right triangle, right angled at D with
As you know, for finding the trigonometric ratios, we need to know the lengths of the sides of the triangle. So, let us suppose that
By Pythagoras theorem,
To find
We know that,
Therefore
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