Question

√√3

In a right triangle, the tangent of one of the two acute angles is 3
What is the tangent of the other acute angle?
O 31√3
O√3/3
O-31√3
O-√3 13

Answer 1

Explanation:

Let's call the angle whose tangent is 3 as angle θ. The tangent of angle θ is given as 3.

Now, let's find the tangent of the other acute angle, which we'll call angle α.

In a right triangle, the sum of the angles is 90 degrees. So, θ + α = 90 degrees.

We know that the tangent of θ is 3, which means:

tan(θ) = 3

Now, we can find the tangent of α using the tangent addition formula:

tan(θ + α) = tan(90 degrees)

Using the tangent addition formula:

tan(θ + α) = (tan(θ) + tan(α)) / (1 - tan(θ) * tan(α))

We know that tan(θ) is 3:

3 + tan(α) / (1 - 3 * tan(α))

Now, we can solve for tan(α):

3 + tan(α) = 0

tan(α) = -3

So, the tangent of the other acute angle α is -3.

Among the given options, the correct one is:

O -√3 13