Maryam's rectangular bedroom is 9 feet by 12 feet. What is the diagonal distance from one corner to the opposite corner?

1 answer:

4 0

Create a right triangle with the the two legs being sides of 9 and 12...then use the Pythagorean theorem to solve

a^2 + b^2 = c^2

9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2

Square root both sides to get c = 15 feet.

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$\begin{array}{rcl}\cos A &=& \dfrac{b^{2} + c^{2} - a^{2}}{2bc}\\\\& = & \dfrac{13.7^{2} + 12.2^{2} - 11.4^{2}}{2\times 13.7 \times 12.2}\\\\& = & \dfrac{187.69 + 148.84 - 129.96}{334.28}\\\\&=& \dfrac{206.57}{334.28}\\\\& = & 0.6180\\A& = & \arccos 0.6180\\& = & \mathbf{51.83 ^{\circ}}\\\end{array}$

2. ∠B

$\begin{array}{rcl}\cos B &=& \dfrac{a^{2} + c^{2} - b^{2}}{2ac}\\\\& = & \dfrac{11.4^{2} + 12.2^{2} - 13.7^{2}}{2\times 11.4 \times 12.2}\\\\& = & \dfrac{129.96 + 148.84 - 187.69}{278.16}\\\\&=& \dfrac{91.11}{278.16}\\\\& = & 0.3275\\B& = & \arccos 0.3275\\& = & \mathbf{70.88 ^{\circ}}\\\end{array}$

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