Aladder is placed 30 inches from a wall. it touches the wall at a height of 50 inches from the ground.
the angle made by the ladder with the ground is
degrees, and the length of the ladder is
inches

Draw a diagram  (see attachment)

we can find the length of the ladder first using pythagorean theorem then use cos⁻¹(x) to find the angle measure
or
we can use tan⁻¹(x) to find the angle measure then use cos(x) to find the hyptotonuse
I'll use the first way

alrighty, so we can find the hypotnuse by using pythagoreano therrem which can be used for right triangles
so if legs are a and b and hytponuse is c then
a²+b²=c²

so
legs are 30 and 50
30²+50²=c²
900+2500=c²
3400=c²
sqrt both sides
10√34=c
the length of the ladder is 10√34 in

ok, so we know hyptonuse is 10√34

cos=adjacent/hypotonuse
but we can use cos⁻¹(x)
cos⁻¹(30/(10√34))=x°
use your calculator
59.03≈x°

the degree measure is about 59° and the length of the ladder is 10√34 in or about 59.3in

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