tom rests a 32-foot ladder against the wall the ladder forms a 61degrees angle with the ground. how high up the wall is the ladder?
If you make a right triangle, with the right angle at the wall, the hypotenuse is the 32-foot ladder. The height of the wall is the side opposite the 61° angle. From
sin(θ)=opposite/hypotenuse, we get
opposite = hypotenuse * sin(θ).
Since both θ(=61°) and hypotenuse (32 feet) are known, the height can be calculated.
is this tigonometry?
im only in P R E A L G E B R A omg idk how to do this
Yes, this is the first glimpse into trigonometry, dealing with the basic definitions of the trigonometric ratios.
its difficult
dang and i got a test 2moro!
I am not sure if you are in the right class, but you'll have to sort this out at school.
The answer to the above question is actually quite simple if you have a calculator.
If h=height in feet
then
sin(61°)=h / 32
therefore
h=32 sin(61°)
= 32 * 0.8746
= 27.99 ft.
The ratio of sin(θ)=opposite/hypotenuse is constant for the same angle θ, irrespective of the length of the hypotenuse.
Don't be intimidated by the Greek letter θ, it's just a symbol, we could as well used x instead.
In Pre-Algebra, we could have formulated the question as follows:
A 32-foot ladder rests against a vertical wall such that the ladder makes an angle of 61° with the horizontal. Knowing that the ratio of opposite / hypotenuse for a 61° right triangle is 0.8746, find the height of the wall at which the ladder leans against it.
The value of 0.8746 can be found from a scientific calculator, most of the time by entering 61 followed by the sine key.