Question

Suppose you have a ladder 6.9 m long, if the latter makes an angle of 63° with the level ground when it is lean against the vertical tower, how high up the tower is the top of the ladder.

Answer 1

To determine the height the ladder reaches on the tower, use the sine function with the length of the ladder and the angle it makes with the ground. Multiply the length of the ladder (6.9 m) by the sine of 63° to get the height.

Step-by-step explanation:

To find out the height at which the top of the ladder reaches the tower, we can use trigonometry, specifically the sine function, since we have the angle that the ladder makes with the ground and the length of the ladder. The sine of an angle in a right triangle is equal to the length of the side opposite the angle (height in this case) divided by the hypotenuse (the length of the ladder).

Here's the calculation:

• Let H be the height reached by the ladder on the tower.
• The length of the ladder, L, is 6.9 m.
• The angle with the ground, θ, is 63°.

Using the sine function (sin):

sin(θ) = H / L

H = L * sin(θ)

H = 6.9 m * sin(63°)

We then compute the sine of 63 degrees and multiply by 6.9 m to get the height H.