trigonometry?

Question

a staircase has a diagonal length of 16 ft and a horizontal length of 10 ft. find the angle of elevation of the stair case.how high do the stairs go?

i could not solve this problem can you please show your work thank you

Answer 1

Diagonal length = 16 ft
Horizontal length = 10 ft

Angle of elevation
= cos^-1 (10/16)
= 51.3 deg

Height of stairs
= 16 x sin 51.3 deg
= 12.487 ft

Answer 2

Well, the staircase should make a right angle. Since 16 is the diagonal length, then there's your hypotenuse. If 10 is your horizontal length, there's a leg. Finding the other leg should be how high the stairs reach up to.
16^2 = 10^2 + x^2
Solve for x.

Answer 3

In terms of a right triangle, the diagonal is the hypotenuse, and the horizontal distance is the leg. The angle of elevation can be represented by cosine and these 2 measurements.

cos (A) = 10/16

cos (A) = 5/8

cos^-1(5/8) = A = 51.3

How high the stairs go is done by pythagoras.

16^2 = 10^2 + (X)^2
x = sqrt(156) = 12.49 ft.

Answer 4

The diagonal lenth is your hypotenuse, therefore H=16
Your horizontal lenght and your hypotenuse make up your angle of elevation, "a" or "alpha". Your horizontal lenght is therefore adjacent to alpha, this give yous A=10.

Now by definition:

cos (a) = A/H

or

cos (a) = 16/10

now to find alpha, use arccosine ..

a = arccosine (16/10)

a = 51.3 degrees (approx.)

Remember to set your calculator to "Degree" mode otherwise your numbers won't come out to the ones above.

Now to find the height, you can use Sin (a) = O/H
[O = opposite side of alpha, i.e. the height of the stairs]

or

sin (51.3) = O/16

or 16sin(51.3) = O

O = 12.5 ft. (approx.)

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another way is to use the pathagorean theorem for your right triangle and solve for your missing side.

16^2 = 10^2 + X^2

Good luck!

Answer 5

Cos a=Opp/Hyp
Cos a=10/16
2ndF cos(10/16)=15.13(to 2 dp)

2ndF DMS=51 degrees 19 minutes 4.125 seconds.
Because the 19 mutes in below 30 the 51 stays the same so the angle =

51 DEGREES.

PLEASE NOTE: The 2ndF thing was done using a scientific calculator. Do nothesitate to email me if you have any concerns. I am doing trgonometry in Maths at the moment.

Answer 6

You can find how high the stairs go by using the Pythagorean Theorem.

c^2 = a^2 + b^2
16^2 = 10^2 + b^2
b^2 = 156
b = 12.489 (approx)

The angle of elevation can be used by the trig function definitions...in this case, we'll use cosine.

cos(theta) = adjacent / hypotenuse
cos(theta) = 10 / 16
cos(theta) = 5/8

Use the inverse cosine function to find theta, which is 51.32 degrees (approx)

Answer 7

cosine (x) = 10/16

x = arccos (10/16) = 51.3 degrees

10^2 + height^2 = 16^2
height^2= 256-100
height = 12.5 feet