Question

write an equation you could use to find the length of the missing side of each right triangle. then find the missing length. round to the nearest tenth if necessary. 1. 8 ft, 10 ft, b ft (right triangle) 2. 26 in., 24 in., a in. (right triangle) 3. 18 cm, 15 cm, c cm (right triangle) 4. 14 yd, 28 yd, a yd (right triangle) 5. 50 mm, 50 mm, c mm (right triangle) 6. 64 m, 45 m, c m (right triangle) 7. a, 65 cm; c, 95 cm 8. a, 16 yd; b, 22 yd

Explanation:

Problem 1

Step1: Apply Pythagorean theorem ($a^2 + b^2 = c^2$), here $a = 8$, $c = 10$, find $b$.

$8^2 + b^2 = 10^2$

Step2: Simplify the equation.

$64 + b^2 = 100$

Step3: Solve for $b^2$.

$b^2 = 100 - 64 = 36$

Step4: Take square root.

$b = \sqrt{36} = 6$

Step1: Apply Pythagorean theorem, $a^2 + 24^2 = 26^2$.

$a^2 + 576 = 676$

Step2: Solve for $a^2$.

$a^2 = 676 - 576 = 100$

Step3: Take square root.

$a = \sqrt{100} = 10$

Step1: Apply Pythagorean theorem, $18^2 + 15^2 = c^2$.

$324 + 225 = c^2$

Step2: Simplify.

$549 = c^2$

Step3: Take square root and round to nearest tenth.

$c = \sqrt{549} \approx 23.4$

Answer:

Equation: $8^2 + b^2 = 10^2$, Missing length: $6$ ft

Problem 2