Question

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

Explanation:

Step1: Identify the given sides

Let the hypotenuse $c = 3.05$ and one - side $a=2.48$.

Step2: Use the Pythagorean theorem to find the other side

By the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, so $b=\sqrt{c^{2}-a^{2}}$. Substituting the values, we have $b = \sqrt{3.05^{2}-2.48^{2}}=\sqrt{(3.05 + 2.48)(3.05 - 2.48)}=\sqrt{5.53\times0.57}=\sqrt{3.1521}\approx1.77$.

Step3: Use the cosine function to find the given - angle

Let the angle $\theta$ be the angle adjacent to side $a$. Then $\cos\theta=\frac{a}{c}$. Substituting $a = 2.48$ and $c = 3.05$, we get $\cos\theta=\frac{2.48}{3.05}\approx0.8131$. So $\theta=\cos^{-1}(0.8131)\approx35.6^{\circ}$.

Answer:

The missing side is approximately $1.77$ and the missing angle is approximately $35.6^{\circ}$