AboutPaul Klarreich Expertise I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction.
I can also try (but not guarantee) to answer questions on Abstract Algebra
-- groups, rings, etc. and Analysis -- sequences, limits, continuity.
I won't understand specialized engineering or business jargon.
Experience I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.
Expert: Paul Klarreich Date: 5/6/2008 Subject: plane trigonometry
Question i dont wanna mis it again ,can you check my answer pls.if ive something wrong with this pls help me thanks
A man standing on top of a building sees an automobile on a street below him. The angle of depression is 36°22'. If his eye is 550ft above the level of the automobile,how far is the automobile from him?
Answer
talking about him specifically and not from the building he is standing on, then
cos(36°22') = 550/x
x = 550/cos(36°22')
x = about 683.03ft
But if talking about from the building, then
tan(90° - 36°22') = 550/y
tan(53°38') = 550/y
y = 550/tan(53°38)
y = 405ft
-------------------------------------
When the sun's angle of elevation is 30° the shadow of a post is 6 ft longer than when the angle is 45°. Find the height of the post.
tan(30) = x/y
y = x/tan(30)
tan(45) = (x + 6)/y
y = (x + 6)/tan(45)
Keep in mind that the sun remains at the same height
x/tan(30) = (x + 6)/tan(45)
tan(30)(x + 6) = tan(45)x
(sqrt(3)/3)(x + 6) = 1(x)
(sqrt(3)/3)(x + 6) = x
sqrt(3)(x + 6) = 3x
x + 6 = (3/sqrt(3))x
x + 6 = sqrt(3)x
x - sqrt(3)x = -6
x(1 - sqrt(3)) = -6
x = -6/(1 - sqrt(3))
x = about 8.196 ft long
ANS : about 8 ft tall
It helps to draw it out.
So that i didn't confused, i drew 2 different right triangles.
In a right triangle given a=32.8ft and A=28 deg. 30' 15" solve for b and c?
b = 32.8 / tan(28 30 15)
= 60.4 ft.
c = 32.8 / sin(28 30 15)
= 68.7ft.
Answer Questioner: arthur
Category: Advanced Math
Private: No
Subject: plane trigonometry
Question: i dont wanna mis it again ,can you check my answer pls.if ive something wrong with this pls help me thanks
A man standing on top of a building sees an automobile on a street below him. The angle of depression is 36°22'. If his eye is 550ft above the level of the automobile,how far is the automobile from him?
....................................
Hi, Arthur,
Yes, there is something tricky about each:
.....................
Answer
talking about him specifically and not from the building he is standing on, then
cos(36°22') = 550/x
x = 550/cos(36°22')
x = about 683.03ft
I think your diagram is :
|\Man
| \
| \ x, but I would use r.
| \
550 | \
| 36\
-------C
y, but I would write x.
I think you want to write:
sin 36 = 550/r, NOT cosine.
You probably have your 36 degrees in the wrong place. Basic clue:
ANGLE OF ELEVATION = ANGLE OF DEPRESSION.
..................................
But if talking about from the building, then
>> I think you want to say 'from the BASE of the building.'
tan(90° - 36°22') = 550/y
tan(53°38') = 550/y
y = 550/tan(53°38)
y = 405ft
I think you got this backwards, too.
tan 36 = 550/y, or tan 54 = y/550
-------------------------------------
When the sun's angle of elevation is 30° the shadow of a post is 6 ft longer than when the angle is 45°. Find the height of the post.
Start by writing:
x = shorter shadow.
x+6 = longer shadow.
y = height of post.
|\
| \
| \
y | \
| \
| \
|30or45\
--------
x or x+6
Now the longer shadow goes with the SMALLER angle of elevation. [Ever take a walk at an hour before sundown? Low sun, long shadow, etc.]
tan(30) = x/y << I think that's y/(x+6)
y = x/tan(30)
tan(45) = (x + 6)/y << I think that's y/x
......................
OK, I think it is time for you to do these over. Then send your solutions.
