A ladder is placed against a wall with an angle between the ladder and the ground of 76°. If the ladder must reach 10 m up the wall, how long does the ladder need to be?

i don't know where to start

Your start would be to make a diagram

of the right-angled triangle.

Then you should see that if L is the length of the ladder,
sin76° = 10/L
L = 10/sin76° = 10.306 m

To find the length of the ladder, we can use trigonometry. In this case, we can use the sine function.

The sine function relates the opposite side of a right triangle to the hypotenuse. In this scenario, the opposite side is the height of the wall (10 m) and the hypotenuse is the length of the ladder that we're trying to find.

We can use the equation sin(θ) = opposite/hypotenuse, where θ is the angle between the ladder and the ground.

Rearranging the equation, we have hypotenuse = opposite / sin(θ).

Now let's substitute the given values:

opposite = 10 m
θ = 76°

hypotenuse = 10 m / sin(76°)

Calculating this value, we find that the length of the ladder needs to be approximately 10.4 m.