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?

Question

19-09-2022
Mathematics

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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?

Answer :

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QWTiffany QWTiffany · Answer 1 · 2022-09-22T07:40:43-04:00

The height of house is 136.83 inches.

As per the given information, height of house will be height or perpendicular of the right angled triangle. The ladder will act as hypotenuse and distance between ladder and house will be the base of triangle.

Now, as the base angle is 60°, the appropriate trigonometric relation that can be used is -

sin theta = perpendicular ÷ hypotenuse

Keep the values in above mentioned relation to find the value of perpendicular or height of house.

sine 60° = perpendicular ÷ 158

Perpendicular = 158 × (✓3/2)

Perpendicular = 79 × 1.73

Perpendicular = 136.8320

Rounding off to nearest hundredth, we get the value = 136.83

Therefore, the height of house is 136.83 inches.

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The complete question is -

A ladder leans against a house at a 60° angle to the ground. House with a ladder measuring 158 inches forming a right triangle. The base angle formed by the ladder is 60 degrees. 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?