PT - Pythagorean

A right triangle ABC has hypotenuse c and legs a, and b of the following lengths. Estimate the length of its remaining side and compare your estimates with your calculations.

a) a = 4 cm; b = 5 cm
b) a = 6.8 m; b = 9 m
c) a= 8.9 m; b = 1 m
d) b= 10 cm; c = 20 cm
e) b=2.5 m; c = 400 cm

Final Answer:

c₁ =  6.4031 cm
c₂ =  11.2801 m
c₃ =  8.956 m
a₄ =  17.3205 cm
a₅ =  3.1225 m

Step-by-step explanation:

$$\begin{gathered} c^2=a^2+b^2 \\ {c}_1=\sqrt{4^2+5^2}=\sqrt{41}=6.4031\text{cm} \end{gathered}$$

$c_2=\sqrt{6.8^2+9^2}=11.2801\text{m}$

$c_3=\sqrt{8.9^2+1^2}=8.956\text{m}$

$a_4=\sqrt{20^2-10^2}=10\sqrt{3}=17.3205\text{cm}$

$$\begin{gathered} b_5=2.5\text{m} \\ {c}_5=400\text{cm}\to \text{m}=400:100\text{m}=4\text{m} \\ {a}_5=\sqrt{c_5^2-b_5^2}=\sqrt{4^2-2.5^2}=3.1225\text{m} \end{gathered}$$

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