A 39-foot tall ladder leans up against a building so that the angle between the ground and the ladder is 89°. How high does the ladder reach up the side of the building? Round to nearest hundredth

Answer 1

/|

L -> / |

A. / |

D. / |

D / | <-- WALL

E / |

R /______|

GROUND

The angle of 89 degrees is at the lower left corner of the above triangle.

We are given the length of the ladder, 39 feet. In the above diagram, the ladder serves as a hypotenuse. The wall height is the side opposite to the given angle.

The sine function can be defined in many different ways. One way is "SOH". SOH stands for Sine-Opposite-Hypotenuse. It means

sine = opposite / hypòtenuse.

To use it if you have the hypotenuse and the angle across from the leg sought, use a little algebra and you will obtain

opposite = sin(89 degrees) × hypotenuse

(The "opposite" refers to the leg of the triangle opposite to the given angle.)

Plugging in our given values

opposite = sin (89º)× 39 feet

and this makes it easy to find the height of the building where the ladder touches.

So the use of SOH is helpful because it provides a formula relating the angle, the hypotenuse, and one of the two legs of right triangle.

SOH is one part of SOH-CAH-TOA. You will soon find out about the rest of this tool in your math class.

Note: 89 degrees is so close to 90 degrees, it would not be useful for leaning a ladder on a wall. This is not a well-thought out problem. But it does give you some basic practice in using SOH.

Answer 2

The answer is 39 × sin 89° feet. As sin 89° is about 0.99985, the calculation depends more on rounding than anything else, and rounds to 38.99 to the nearest hundredth, and 38.994 to the nearest thousandth.

I can't draw on the screen as part of my answer, so I cannot illustrate why the answer is 39 × sin 89°.You will have to take my word on that; it follows from the definition of the sine function.