A 15-foot ladder leans against a wall and makes an angle of 65° withthe ground. What is the horizontal distance from the wall to the baseof the ladder, to the nearest tenth of a foot?
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Given:
Hypotenuse = 15 feet
We can picture out this problem as right triangle, whereas the hypotenuse is the ladder leaning to the wall.
Angle of the ladder and the ground = 65°
Find the horizontal distance from the wall to the base of the ladder.
Solution:
In order to find the horizontal distance from the wall to the base of the ladder, we simply need to solve using the SOHCAHTOA,
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
In our case since we are asked to find for the base, which is adjacent to the angle, we can use Cosine.
Let a = adjacent side.
Cos 65° = a/15
Multiply both sides by 15 in order to cancel out a/15 leaving behind a.
(15) Cos 65° = a/15 (15)
a = 15 Cos 65°
a =6.34 feet
Final answer:
The distance from the wall to the base of the ladder is 6.34 feet.