Lesson 8: Measurement and Geometry
Graded Assignment \#8: Measurement and Geometry
Please solve each of the questions below: Each question will be worth 2 points
1.
Find the missing angle and side measures of $\triangle A B C$, given that $m \angle A=25^{\circ}$, $m \angle C=90^{\circ}$, and $C B=16$.
2.

Step 1 ：Given that $m \angle A=25^{\circ}$, $m \angle C=90^{\circ}$, and $C B=16$.

Step 2 ：Since the sum of the angles in a triangle is $180^{\circ}$, we can find the missing angle B by subtracting the given angles from $180^{\circ}$. This gives us $\angle B = 180^{\circ} - 25^{\circ} - 90^{\circ} = 65^{\circ}$.

Step 3 ：Since $\angle C$ is $90^{\circ}$, the triangle is a right triangle. We can use the Pythagorean theorem to find the missing sides. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this rule as: $a² + b² = c²$.

Step 4 ：In this case, side $CB$ is the hypotenuse. We can find side $AC$ (opposite to angle B) using the sine of angle A (since $\sin(A) = \frac{opposite}{hypotenuse}$) and side $AB$ (adjacent to angle B) using the cosine of angle A (since $\cos(A) = \frac{adjacent}{hypotenuse}$).

Step 5 ：Calculating these values gives us $AC \approx 6.76$ units and $AB \approx 14.50$ units.

Step 6 ：\(\boxed{\text{Final Answer: The missing angle B is } 65^{\circ}, \text{ side AC is approximately } 6.76 \text{ units, and side AB is approximately } 14.50 \text{ units.}}\)