Can someone help me anser answer this trig question and make a drawing using symbols of the problem in the ans

Question

straight path makes an angle of 6degrees with the horizontal. A statue at the higher end casts a 6.5 meter shadow straight down the path. The angle of elevation from the end of the statue to the top of the shadow is 32 degrees. How tall is the statue?

Answer 1

Assuming the angle of elevation is from the "end of the SHADOW to the top of the STATUE" (and not the reverse as written)...

You have a rising path (on which the shadow is projected). I can't draw a good diagram with ASCII characters, but the problem is like two wedges stacked on top of each other -- the bottom one is the rising path, and the top one is the line of sight up to the top of the statue.

The shadow is a hypotenuse of a right triangle with a 6 degree angle. The horizontal distance from the end of the shadow to the point under the base of the status is 6.5 * cos(6 degrees) = 6.4644. The rise in the path over that distance is 6.5 * sin(6 degrees) = 0.679 meters.

The line of sight up to the statue is the hypotenuse of a right triangle with a (6 + 32) degree angle, with the adjacent side 6.4644 meters (as calculated above). tan(38) = x/6.4644 where x is the sum of the rise in the path and the height of the statue.

Solving for x, we get x = 5.0505m. Subtracting the rise in the path, we get 4.37 meters for the height of the statue.

Answer 2

draw a right triangle with the 90 deg corner in the lower right of the triangle.

from the lower right corner of the triangle, you need to draw a vertical and horizontal line starting at the lower right corner.

from some point (call is point A) along the horizontal line, draw a line at 6 deg from the horizontal until it intersects the vertical line. The length of the sloping line represents the 6.5 meter shadow. Now from point A draw another angle of 32 deg as measured from the line which represents the shadow and intersect this line with the vertical line of the triangle. Let's call the 90 degree corner Point B. Point C is the intersection of the line from point A to the vertical line from point B.

Extend the vertical line up a little bit and stop. We will call this Point D. Now connect point D to Point A to finish the larger triangle. Now we have triangle ABD with ABC inside of it.

The length of line AC is 6.5 m by definition, and the angle BAC = 6 degrees by def and angle CAD = 32 deg by def.

Angle BAC = 84 degrees since we have 6 at BAC and a 90 deg angle at the lower right corner.

From this triangle BAC, the hypotenuse is 6.5 m, but we need to calculate length CD which represents the height of the statue. Let's look at triangle ACD. We know angle BAC = 32 deg and that length AC = 6.5 m. Also that angle BAD = 32+6 = 38 degrees. Also we know that angle DCA = 180-84 = 96 degrees.

From the sine law we can write that sin 52/6.5 = sin 32/CD

and CD = 4.371 m which is the height of the statue.

Answer 3

Two of us already answered this question the best we can. We can't put graphics on this forum. Email me privately (off my profile) and I can try to send you a picture.

Answer 4

i actually drew a diagram,, give me your e-mail so can send it over,,

dont worry its clean!!!!!!!!!!!!!

[e-mail] mail me ,, ill send it over