Question

Janelys leans a 16-foot ladder against a wall so that it forms an angle of 61^{\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.

Answer 1

The height the ladder reaches up the wall is $13.99ft$

The ladder, the wall, and the ground form a right-angled triangle.

The ladder is the hypotenuse, or the longest side, of the triangle. The wall is opposite of the angle, $61^{\circ}$, that the ladder makes with the ground.

The formula relating the angle the ladder makes with the ground, the ladder, and the wall is the trigonometric ratio

$sin 61^{\circ}=\dfrac{\text{wall height}}{\text{ladder length}}$

substituting the values for the ladder length, and $sin61^{\circ}$, and solving, we get

$0.8746=\dfrac{\text{wall height}}{16}\\\\\text{wall height}=0.8746\times16\approx13.99ft\text{ (to the nearest hundredth)}$

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