A roofer props a ladder against a wall so that the top of the ladder reaches a 20 foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is 46 degrees, what is the length of the ladder to the nearest foot?

19.33 ft

Step-by-step explanation:

This analogy has to do with Pythagoras theorem.

We're given our angle of elevation to be 46°, and told that the height of the building to be 20 ft. Using Pythagoras theorem, we know that the given height is opposite to the angle of elevation, and thus, the required distance is adjacent to it.

Sin 46° = opp / hyp

Sin 46° = 20 / hyp

hyp = 20 / sin 46

hyp = 20 / 0.719

hyp = 27.82 ft

We've gotten the length of the ladder, our hypotenuse, to be 27.82. It's tied length we'd then use top find the needed length.

Cos 46° = adj / hyp

Cos 46° = adj / 27.82

adj = 27.82 * Cos 46

adj = 27.82 * 0.695

adj = 19.33 ft

Therefore, the required length is approximately equal to 19.33 ft

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