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Katherine leans a 30-foot ladder against a wall so that it forms an angle of
72^(@) with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
◻ feet

Katherine leans a $30$ -foot ladder against a wall so that it forms an angle of $72^{\circ}$ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary. $\newline$ $\square$ feet

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Experiment design

Full solution

Q. Katherine leans a

30

-foot ladder against a wall so that it forms an angle of

72^{\circ}

with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.

\newline

\square

feet

Given information: We have a $30$ -foot ladder and an angle of $72$ degrees with the ground. We're looking for the height up the wall, which is the opposite side in a right triangle.
Sine function calculation: We can use the sine function, which is $\frac{\text{opposite}}{\text{hypotenuse}}$ . So, $\sin(72) = \frac{\text{opposite}}{30}$ .
Solving for opposite side: Now we solve for the opposite side: $\text{opposite} = 30 \times \sin(72)$ .
Calculating sine of $72$ degrees: Using a calculator, $\sin(72)$ is approximately $0.95105$ . So, opposite $\approx 30 \times 0.95105$ .
Final calculation: Multiplying $30$ by $0.95105$ gives us $28.5315$ feet.
Rounding to nearest hundredth: Rounding to the nearest hundredth, the ladder reaches approximately $28.53$ feet up the wall.

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