Question

In this triangle, the product of tan A and tan C is __________. (1, 4.24, 17.98, Insuficciant Date)

Answer 1

For this triangle, tan(A) · tan(C) = 1.

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

`\displaystyle\rm \tan{\hat{A}} = \frac{\text{Opposite}}{\text{Adjacent}} = (BC)/(AB)`.

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,

`\displaystyle \rm \tan{\hat{A}} = (BC)/(AB) = 1`.

Similarly,

`\displaystyle \rm \tan{\hat{C}} = (AB)/(BC) = 1`.

The product of tan(A) and tan(C) will therefore equal to 1.