Geometry questions, i need help!!! ?

Question

A building casts a 200 ft long shadow. At the same time, your shadow is 5 feet long. You are 6 feet tall. How tall is the building?

a 6.7 ft

b 100 ft

c 166.6 ft

d 240 ft

Determine if the given measures are sides of a right triangle: 9, 10, 15

yes

or no?

cos A = .7986, find angle A.

tan R = 4.0108, find angle R.

Write an equation for a circle with center at P(2, -5) and a diameter of 8 units.

these are the last questions on my quiz, i dont get any of them, xplanations would be nice, thanks

for the last question, the choices are

a. (x - 2)2 + (y - 5)2 = 64

b . (x + 2)2 + (y + 5)2 = 8

c . (x - 2)2 + (y + 5)2 = 16

d. (x + 2)2 + (y - 5)2 = 16

Answer 1

Prob 1: (d) 240

Do comparative triangles... for every 5 ft horizontal you need to go 6 ft vertically so 200/5*6 = 240.  

This can be verified by using one of the angles in the 5x6 triangle to compare to the 200x? triangle

tan (x) = 6/5

x =tan^(-1)(6/5) = 50.1

tan(50.1) = y/200

tan(50.1)*200 = y

Prob 2: No

A right triangle agrees with a^2 +b^2 = c^2

So take the two smaller numbers and try this out.

9^2+10^2 = 81+100 = 181

sqrt (181) = 13.45 therefore this is not a right triangle

Prob 3: cos A = .7986

A = cos^(-1) of (.7986) = 37.00 degrees

Prob 4: tan R = 4.0108

R = Tan^(-1)(4.0108) = 76.00 degrees

Prob 5: The standard equation of a circle with center (h,k) and radius r is as follows:

(x - h)^2 + (y - k)^2 = r^2

The radius is half of the diameter = 8/2 = 4

h = 2

k = -5

Therefore the answer is (c)  (x-2)^2+(y+5)^2 = 4^2 = 16

Hope this helps . . . b.