How do I figure out this problem?

Question

Sin, Cos, Tan...

A 10-foot ladder leans against a wall so that the base of the ladder is 8 feet from the base of the building. What angle does the ladder make with the ground?

I already have AB as 10 ft, CB as 8 ft, and a 90 degree angle formed with the ground and wall. How do I use sine, cosine, or tangent to figure out the angle the ladder makes with the ground?

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Answer 1

Let theta be the angle that the ladder makes with the ground. The ladder is the longest side so it's the hypotenuse and the length from the ladder to the building is the adjacent.

From SOHCAHTOA, we know that we need to use Cosine.

Cos(theta)= adj/hyp=8/10=0.8

Take ArcCos of both sides (inverse cosine).

You should get 36.87 degrees.

Answer 2

The angle that the ladder makes with the ground would be arccos (8/10) which is approx 36.87 degrees.
To get the sin, cos, and tan, draw the picture, and use the pythagorean theroem to find the missing side. Then use the definitions of the trig functions, as ratios of sides in a right triangle, to find the sin, cos, and tan.
8^2 + x^2 = 10^2
64 + x^2 = 100
x^2 = 36
x = 6
So your angle, call it theta, has a sin of 6/10 or 3/5 and a cosine of 8/10 or 4/5. Your tangent is 6/8 or 3/4. This is a double of the familiar 3:4:5 pythagorean relation.

Answer 3

You already have AB as 10 ft, CB as 8 ft, and a 90 degree angle formed with the ground and wall.

Your given is the adjacent side of the angle say theta and a hypotenuse.

so using cosine theta = adjacent / hypotenuse

cos theta = 8 ft / 10 ft = .8

angle theta = arccos .8

you will get 1 degree

Answer 4

first, using pythorgeon theorem (c^2 =a^2 + b^2) 10 = 100, 8 = 64 c^2 - a^2 = b^2,100 - 64 = 36; square root of 36 = 6
the triangle is now 6 ft by 8 ft by 10ft, with a right angle
use theta:
sin(theta) = 8/10; cos(theta) = 6/10; tan(theta) = 8/6.
All three come to 53.13 degrees on the ground angle
now take 53.13 away from 90degrees = 38.87degrees for the top angle on the wall the latter is sitting on.
On your TI-84, push the 2nd function key then push any of the three trig functions with their assigned fractions to get 53.13 degrees, after you get your answer, push 2nd function again and the enter key and the calculator will set 90-53.13, then push enter one more time and it will give you the other angle.

Answer 5

suppose you have a righttriangle ABC right angled at B
aide ACis known as the hypotenuse
if you select angle A as yourreference angle BC is known as theopposite side and AB the adjacent side
now the ratio of AB/AC is known as sinA
BC/AC is known as cos A
AB/BC is known as tanA

if we choose angle B as the reference angle BC willbe the opposite side and AB the adjacent side
so BC/AC=sinB
AB/AC=cosB
BC/AC=tan B
suppose the angle the ladder makes with the ground is x
8/10=cos x
cosx=0.8
so find the angle for which the cos ratio is0.8
that is your answer

Answer 6

sine (angle) = side opposite to the angle/hypotenuse

cosine (angle) = adjacent side/hypotenuse

tangent (angle) = opposite/adjacent