Question

For safety reasons, the angle between a ladder and the ground should be between 65 and 80 degrees. A ladder that is 5m long is placed so that it reaches a window on the top floor of a house. If the foot of the ladder is 1.5m from the house, is the ladder safe? Any help is greatly appreciated.

Answer 1

Do you know your trigonometric functions?

Answer 2

Ehh.. not really :/

Answer 3

You have sine, cosine, and tangent.

The sine of an angle is equal to the side of the triangle opposite the angle divided by the hypotenuse (the side across from the 90 degree angle)

The cosine of an angle is equal to the side of the triangle adjacent to the angle (the one touching it that isn't the hypotenuse) divided by the hypotenuse

The tangent of an angle is equal to the side of the triangle opposite the angle divided by the side adjacent to the angle

For short you can memorize this by

SOH CAH TOA
- Sine = Opposite/Hypotenuse
- Cosine = Adjacent/Hypotenuse
-Tangent = Opposite/Adjacent



Now on your triangle we have the side adjacent to the angle and the hypotenuse



So we need to use the trigonometric function with adjacent and hypotenuse CAH
cos(angle) = 1.5/5 = 0.3

Now on your calculator you should have a function that looks like cos^-1(angle)
This is called the inverse cosine and if you use it on one of these ratios it will give you the angle that made it

cos^-1(0.3) = 72.54

*Don't forget to put your calculator in degrees

Answer 4

I'm looking on my calculator i only seem to have Cos and not Cos-1 :/

Answer 5

Never mind! Had to press Shift before hitting Cos

Answer 6

Thank's a lot for the help! Helped me a lot!

Answer 7

Yup :)