Answer: 9.32 ft
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Cos α = adjacent side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the adjacent side (x) is the distance between the bottom of the ladder and the house.
Replacing with the values given:
cos 39 = x/ 12
Solving for x
cos39 (12) =x
x= 9.32 ft
Feel free to ask for more if needed or if you did not understand something.
Answer:
The bottom of the ladder is 7.55 feet far away from the house
Step-by-step explanation:
To find the distance between the bottom of the ladder from a house if a ladder of 12 feet long is leaning against a house at an angle of 39°, then we will follow the steps below:
We can use trig ratios to find the solution to this problem
SOH CAH TOA
sinФ= opposite/hypotenuse
cosФ=adjacent/hypotenuse
tanФ=opposite /adjacent
from the diagram below;
angle Ф=39°
hypotenuse =12 feet
opposite = x where x is the distance of the bottom of the ladder from the house
Given these parameter, the best trig function to use sine
sinФ = opposite / hypotenuse
sin 39° = [tex]\frac{X}{12}[/tex]
cross-multiply
x = 12 sin 39
x ≈ 7.55 feet
Therefore, the bottom of the ladder is 7.55 feet far away from the house
