Answer:
height = 9.19 ft
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
Or
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)