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a.
To complete the table using
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Concept used:
Hypotenuse is the longest side of the right triangle.
Perpendicular is the line at an angle of
Base is the side of the right triangle on which the right angle stands.
Relationship between angles and the sides of the triangle is given by,
Calculation:
In triangle ABC,
Hypotenuse
Perpendicular
Base
In triangle JKL,
Hypotenuse
Perpendicular
Base
In triangle XYZ,
Hypotenuse
Perpendicular
Base
Substituting for the hypotenuse, base and perpendicular by applying the concept of sine, cosine and tangent of an angle,
Triangle | Trigonometric Ratios | ||||
ABC | 1 | ||||
1 | |||||
JKL | 1 | ||||
1 | |||||
XYZ | 1 | ||||
1 |
Conclusion:
The table is filled using the basic definitions of sine, cosine and tangent of an angle.
b.
To make a conjecture on the squares of sine and cosines of a right triangle.
b.
![Check Mark](/static/check-mark.png)
Answer to Problem 50PPS
The sum of the squares of the sine and cosine of an acute angle of a right triangle is 1.
Explanation of Solution
By the general identities of trigonometry, the sum of the squares of the sines and cosines of an acute angle of a right triangle is 1.
Chapter 10 Solutions
Algebra 1
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