Answer:
For this triangle, tan(A) · tan(C) = 1.
Step-by-step explanation:
In a right triangle ABC, if
- A is an acute angle,
- B is a right angle,
BC will be the side opposite to angle A. AB will become the side adjacent to angle A.
The tangent of A will equal to
[tex]\displaystyle\rm \tan{\hat{A}} = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{BC}{AB}[/tex].
The two acute angles of the right triangle in this question are equal. As a result, this right triangle is an equilateral right triangle. AB = BC. Therefore,
[tex]\displaystyle \rm \tan{\hat{A}} = \frac{BC}{AB} = 1[/tex].
Similarly,
[tex]\displaystyle \rm \tan{\hat{C}} = \frac{AB}{BC} = 1[/tex].
The product of tan(A) and tan(C) will therefore equal to 1.
