Question

label the sides and angle and calculate the missing values in the triangle:

Explanation:

Step1: Assume it's a right - triangle and use Pythagorean theorem

Let the two given sides be $a = 1.61$ and $b = 1.98$. If the missing side is the hypotenuse $c$, then by the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$. If one of the given sides is the hypotenuse, we use $c^{2}-a^{2}=b^{2}$ to find the other side. Let's assume the two given sides are the legs of the right - triangle. Then $c=\sqrt{1.61^{2}+1.98^{2}}=\sqrt{2.5921 + 3.9204}=\sqrt{6.5125}\approx2.55$.

Step2: Find an angle

We can use the tangent function to find an acute angle. Let $\theta$ be an acute angle. $\tan\theta=\frac{1.61}{1.98}\approx0.8131$. Then $\theta=\arctan(0.8131)\approx39.1^{\circ}$. The other acute angle is $90^{\circ}-39.1^{\circ}=50.9^{\circ}$.

Answer:

The missing side is approximately $2.55$. One non - right angle is approximately $39.1^{\circ}$ and the other is approximately $50.9^{\circ}$.