A 13 ft ladder is resting on a wall. The angle the ladder makes with the floor is 45 degrees. How high off the ground is the top of the ladder? Use the function y=13cos(theta) to find the answer

height = 9.19 ft

Step-by-step explanation:

The ladder is resting on a wall. The angle the ladder makes with the floor is 45°. The ladder is 13 ft. The illustration forms a right angle triangle.

The hypotenuse side of the right angle triangle is 13 ft . The opposite side of the right angle triangle is the unknown which is the height off the ground the top of the ladder. Therefore,

Using ratio

sin ∅ =  opposite/hypotenuse

sin ∅ = opp/13

sin 45° = opp/13

cross multiply

13 sin 45 = opp

opp = 13 × 0.70710678118

opp = 9.19238815543

height = 9.19 ft

You can use the following base on your equation(y = 13 cos ∅)

The other angle will definitely be 45° since total angle in a triangle is 180°. 180 - 90 - 45 = 45°.

The adjacent side of the triangle will be the unknown side if we use cosine ratio.

cos ∅ = adjacent/hypotenuse

cos 45° = adjacent/13

cross multiply

From your equation you represented adjacent as y therefore,

y = 13 cos 45°

y = 13 × 0.70710678118

y = 9.19238815543

y = 9.19 ft (which is the required height)