You have a 15 ft

Question

You have a 15-foot ladder that you are using as you paint your house. You place the ladder so that it forms an angle of 35 at the point of contact between the ladder and the ground. How high will the top of the ladder be above the ground? (3 points for drawing + 3 points for correct answer= 6 points total) Draw a diagram of this word problem (use a right triangle).Let h denote the height of the ladder against the house. Calculate h using the sine function and your calculator.

Answer 1

For the first part you want to draw a diagram where

1. the ladder (length 15 ft) leans against the house and makes a 35° angle with the ground
2. the ladder forms the hypotenuse of a right triangle
3. the ground under the ladder forms the side of the right triangle adjacent to the 35° angle
4. the house behind the ladder forms the side of the right triangle opposite to the 35° angle

The length of the opposite side of your right triangle is how high the top of the ladder will be above the ground.

sin(35°) = opposite/hypotenuse = (height of the top of the ladder above the ground)/(length of the ladder)

So the height of the top of the ladder above the ground = (length of the ladder) × sin(35°)

Calculate sin(35°), then multiply it by the length of the ladder and you have your answer.