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What is the height of the tent?

What is the height of the tent?

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Area and perimeter: word problems

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Q. What is the height of the tent?

Identify Formula: Step $1$ : Identify the formula to use for calculating the height of the tent. $\newline$ For a right-angled triangle, the Pythagorean theorem states that the square of the hypotenuse $c$ is equal to the sum of the squares of the other two sides $a$ and $b$ . The formula is $c^2 = a^2 + b^2$ .
Plug in Values: Step $2$ : Plug in the known values into the Pythagorean theorem. $\newline$ We know the hypotenuse $c$ is $10$ meters and the base $a$ is $8$ meters. We need to find the height $b$ . $\newline$ $10^2 = 8^2 + b^2$
Calculate Squares: Step $3$ : Calculate the square of the known sides. $\newline$ $10^2 = 100$ $\newline$ $8^2 = 64$ $\newline$ Now we have $100 = 64 + b^2$ .
Isolate Variable: Step $4$ : Isolate the variable $b^2$ to solve for $b$ . $\newline$ Subtract $64$ from both sides of the equation to get $b^2$ by itself. $\newline$ $100 - 64 = b^2$ $\newline$ $36 = b^2$
Find Value: Step $5$ : Find the value of $b$ by taking the square root of both sides. $\sqrt{36} = \sqrt{b^2}$ $6 = b$
Final Answer: Step $6$ : State the final answer. $\newline$ The height of the tent is $6$ meters.

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