A 3m ladder is leaning against a vertical wall, the angle between the ground the ladder is pi/3. what is the exact height that the ladder reaches up the wall?

Question

i dont understand what the question means

Answer 1

Dear Kevin,

     It might be a good idea to draw the right triangle and label all the parts with the given information.

 

You are looking at a right triangle, call it  Triangle ABC.  They are asking for the distance from where the ladder

 

touches the top of the vertical wall to the base of the wall.

 

 

Ladder =3 M =hypotenuse                Let ∠C=angle C = 90 degrees   and  ∠B=angle B= pi/3

 

1/3 pi= 60 degrees   You can convert by saying 180º/3 =60º

 

 

You need to know the length of two sides to use the Pythagorean Equation. You only know the length of the

 

hypotenuse and the radian (pi/3) measure and degree equivalent. Here is a short cut:

 

 

 1.  At this point you will want to recall the special right triangle.  This procedure works for every special right triangle that has a 60º angle.  You just have to memorize three little things.  One of them was the following:  opposite the 60 degree angle is a side with a general measure of X√3.  The total degrees in a triangle is 180, so there are a 30 degree angle and a 90 degree angle.  Opposite the 30 degrees is a side measure of X.  The hypotenuse is 2X, which is equal to 3 M, given in this particular problem.     2X=3 , so X= 3/2=1.5   length of hypotenuse of triangle   

 

2.  Now, just replace X√3, which is the length of the wall, with the value for X, which is 1.5.

 

3.  That gives you 1.5√3=length of the wall.  This answer is an exact answer.

 

 

I hope that this work was helpful for you.  If it was, please give me a thumbs up.

 

                                                                                        Susan C.

 

 

 

 

 

 

Answer 2

 

The question asks how far up the wall the tip of the ladder reaches. The tip of the ladder is touching the wall how far up from the ground ?

The wall, the ground, and the ladder form a right triangle.

The ladder is the hypotenuse and the wall and the ground are the legs.

use the sine function

sin=opposite/hypotenuse

sin(60º)=opposite/3

sin(60º)=√3/2

√3/2=opposite/3

3√3/2=opposite where "opposite" is how far up the wall the ladder reaches

(3)(1.73205)/2=opposite

(5.19615)/2=opposite

2.598075=opposite

the ladder reaches 2.598075 m or approximately 2.6 m up the wall

I just realized the question asked for the exact height. Michael J. has the correct exact height. Look at his solution.

Answer 3

If we draw this ladder in a diagram, we will get the shape of a right triangle.  The length of the ladder forms the hypotenuse of the triangle.  The angle between the ground and the ladder is π/3.  The height of the ladder forms the vertical leg of the triangle.

 

If we label this diagram correctly, we can use the sine trigonometric function.

 

sinθ = (side opposite to angle) / (hypotenuse)

 

 

Plug in the values into the formula.

 

sin(π/3) = (height of the ladder) / 3

 

√(3) / 2 = (height of the ladder) / 3

 

3 * √(3) / 2 = height of the ladder

 

(3 / 2)√(3) = height of the ladder 

 

1.5 √(3) = height of the ladder

 

 

The height of the ladder is 1.5√(3) meters.