Question

1. draw a right triangle that has an angle with a tangent of 1.

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). If \(\tan\theta = 1\), then \(\frac{\text{opposite}}{\text{adjacent}}=1\), so the length of the opposite side and the adjacent side are equal.

Step2: Draw the right - triangle

Let the length of the two legs (the sides adjacent to the right angle) be \(a = b=1\) (we can choose any non - zero value, \(1\) is a simple choice). Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = b = 1\), then \(c=\sqrt{1^{2}+1^{2}}=\sqrt{2}\).

Answer:

Draw a right - triangle with legs of length \(1\) and \(1\) and hypotenuse of length \(\sqrt{2}\). The non - right angles are \(45^{\circ}\) (since \(\tan45^{\circ}=1\)).