Warren is painting his house using a 20 foot ladder. The ladder makes a 60 degree angle with the ground. How high up on the house is the top of the ladder?

Question

I haven't really gotten the hang of Triangles, kinda struggling on it.                                                                                                                                

Answer 1

Hi Troy,

 

Warren is painting his house using a 20 foot ladder. The ladder makes a 60 degree angle with the ground. How high up on the house is the top of the ladder?
I haven't really gotten the hang of Triangles, kinda struggling on it.

 

Troy, it is a very good idea to make a diagram when dealing with word problems and trig.

 

Since the ladder is leaning against the house, it acts as the hypotenuse of a right triangle.

The side we are looking for this the side across from the 60° angle.

 

sin 60°= x/20     now cross multiply

20sin 60^°=x

20·√3/2=10√3 feet

 

ANSWER:  The ladder is 10√3 or 17.32 feet.

 

 

If you didn't know the value of the sin 60°, make sure your calculator is on degree mode rather than radian.  If the calculator is on radian mode, you will get an incorrect response.  Just keep this in mind.

 

Hope this helps you understand the process.

 

 

Answer 2

Draw the diagram of the ladder leaning against the wall of the house.  You will notice a right triangle.  The length of the ladder represents the hypotenuse of the triangle.  The angle between the ladder and the ground is 60 degrees.  The height of the ladder up the house represents the vertical leg of the triangle.

 

Based on this this triangle, we will use the sine trigonometric function.

 

sin(θ) = (height of the ladder) / (ladder length)

 

ladder length * sin(θ) = height of the ladder

 

20 * sin(60) = height of the ladder

 

 

Now just complete the calculation to find the height.