A ladder leans against a house at a 60° angle to the ground.
If the ladder extends to a length of 158 inches, what is the height of the house rounded to the nearest hundredth of an inch? Type the numeric answer only in the box below.

Question

A ladder leans against a house at a 60° angle to the ground. 
If the ladder extends to a length of 158 inches, what is the height of the house rounded to the nearest hundredth of an inch? Type the numeric answer only in the box below.

anonymous · Answer

attachment

anonymous · Answer

This is another 30-60-90 triangle.

This time, the ratio of the height of the house- let's call it h!- to the length of the ladder is going to be $$\sqrt{3}/2$$ 

So $$h/158 = \sqrt{3}/2$$

Cross-multiplying, we get $$2h = 158\sqrt{3}$$

Dividing each side by two, we get$$h = 79\sqrt{3}$$

Which, rounded to the nearest hundredth of an inch, is 273.66 inches.

If you get stuck on problems like this, try looking up 30-60-90 triangles online or in a textbook. Remember that the ratio is 1 to 2 to $$\sqrt{3}$$

anonymous · Answer

so the answer is square root is 3

anonymous · Answer

No, the answer is 273.66 inches.