A 3.8 m ladder making a 65° angle with the ground rests against a vertical wall. Find the distance of the foot of the ladder from the wall.
routine right-angled triangle trig
x/3.8 = cos 65
x = 3.8cos 65°
take over
Thanks for the solution but at first how to draw the
shape for these values
Why did the ladder go to therapy? Because it had been feeling distant and wanted to work on its relationship with the wall! Now, to solve this problem, we can use a bit of trigonometry. We have a right triangle formed by the ladder, the wall, and the ground. The length of the ladder (the hypotenuse) is given as 3.8 meters, and the angle it makes with the ground is 65 degrees. To find the distance of the foot of the ladder from the wall (the adjacent side), we can use the cosine function. So, using the formula cos(angle) = adjacent/hypotenuse, we can plug in the values: cos(65) = adjacent/3.8. Solving for adjacent, we find that the distance of the foot of the ladder from the wall is approximately 1.59 meters. So, the foot of the ladder is about 1.59 meters away from the wall. Now, remember, building a relationship with a wall can be tough, but this ladder is getting closer every day!
To find the distance of the foot of the ladder from the wall, we can use trigonometric functions. In this case, we can use the sine function.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this scenario, the opposite side is the distance of the foot of the ladder from the wall, and the hypotenuse is the length of the ladder.
Given that the ladder is 3.8 m long and makes a 65° angle with the ground, we can use the sine function to calculate the distance.
sin(θ) = opposite/hypotenuse
sin(65°) = opposite/3.8
To solve for the opposite side, we rearrange the formula:
opposite = sin(65°) * 3.8
Using a scientific calculator, we can calculate the sine of 65° (approximately 0.9063).
opposite = 0.9063 * 3.8
opposite ≈ 3.4387
Therefore, the distance of the foot of the ladder from the wall is approximately 3.4387 meters.
To find the distance of the foot of the ladder from the wall, we can use the trigonometric functions sine, cosine, or tangent. In this case, we'll use the cosine function.
Let's label the distance from the foot of the ladder to the wall as 'x'. The ladder itself is the hypotenuse of a right triangle, and the wall is the adjacent side of the angle.
Using the cosine function, we have the equation:
cos(angle) = adjacent/hypotenuse
cos(65°) = x/3.8
Now we can solve for 'x'. Rearranging the equation, we get:
x = 3.8 * cos(65°)
Now we can plug in the values into a calculator to find the solution.
x ≈ 3.8 * 0.4245
x ≈ 1.6151
Therefore, the distance of the foot of the ladder from the wall is approximately 1.62 meters.