A ladder leaning against a vertical wall makes a angle of 75degree with the ground. If the foot of the ladder is 4 feet from the base of the wall, would this ladder be long enough for you to retrieve the suction dart that your friend stuck 17ft up the wall?
First set up a right triangle:
/)
H / ) X (wall)
/ )
/75____)
4 (distance from ladder to wall)
ladder=H
distance from ladder to wall=4
height of wall=X
We know that the ladder and the ground make a right triangle so we can use trig functions to solve.
since tan is opposite side over adjacent side we have this so far:
tan75=X/4
4tan75=X (multiply both side by 4)
type that into your calculator and you should get about 15 feet.
Does this answer your question?
sorry I tried to make a diagram up there but it turned into jibberish when I posted.
Also I forgot to put that the angle between the ladder and the ground is 75.
9. An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle.
a 12-foot ladder rests against the side of a house.the base of the ladder is 3 feet away from the side of the house.how high above the ground is the top of the ladder? round to the nearest of a foot
The base of a ladder should be placed 3 feet from the wall for every 5 feet of ladder length. How many a ladder is needed to safely reach 36 feet above ground?
To determine if the ladder is long enough to reach the suction dart on the wall, we can use trigonometry. Here's how you can find the length of the ladder:
1. Draw a right-angled triangle with the ladder as the hypotenuse (longest side), the wall as one side, and the ground as the other side.
2. The angle between the ladder and the ground is given as 75 degrees.
3. The distance of the foot of the ladder from the base of the wall is 4 feet.
4. The height at which the dart is stuck is given as 17 feet.
Now, we can apply the trigonometric function tangent (tan) to find the length of the ladder:
Tan(angle) = Opposite side / Adjacent side
Tan(75 degrees) = 17 feet / 4 feet
To solve for the length of the ladder, multiply both sides by 4 feet:
4 feet * Tan(75 degrees) = 17 feet
Using a calculator, determine the value of Tan(75 degrees). It is approximately 3.732. So, the equation becomes:
4 feet * 3.732 = 17 feet
The left side simplifies to 14.928 feet. Since 14.928 feet is less than 17 feet, it means that the ladder is not long enough to retrieve the suction dart from the wall.