Question

1. calculate the length of side ( c ) in a right triangle with legs 15cm and 20cm.2. calculate the length of side ( b ) in a right triangle with hypotenuse 78cm (one leg is the side adjacent to the right angle, the length of the other side is not shown).3. calculate the length of side ( a ) in a right triangle with hypotenuse 51cm and one leg 45cm.4. calculate the length of the unknown side in the right triangle with one side 60cm (the other side and hypotenuse are not fully shown).

Explanation:

Step1: Calculate $c$ via Pythagoras

$$c=\sqrt{15^2 + 20^2}=\sqrt{225+400}=\sqrt{625}=25\mathrm{cm}$$

Step2: Calculate $a$ via Pythagoras

$$a=\sqrt{51^2 - 45^2}=\sqrt{2601-2025}=\sqrt{576}=30\mathrm{cm}$$

Step3: Note unsolvable cases

For the triangle with side $b$, only one side (78cm) is given, so $b$ cannot be found. The bottom triangle is missing side length information, so its unknown cannot be calculated.

Answer:

$c=25\mathrm{cm}$, $a=30\mathrm{cm}$ (Note: The value of $b$ cannot be calculated as one side length is missing; the bottom triangle is incomplete so its unknown cannot be solved)