Don L. answered • 02/23/17
Tutor
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(18)
Fifteen years teaching and tutoring basic math skills and algebra
Hi Casey, solve this using the law of signs, a/sin a = b/sin b = c/ sin c.
We are given two angles, 40 to the top of the sign and 32 degrees to the bottom of the sign from a point on the sidewalk. From the point on the sidewalk where the 40 degree angle and 32 degree angle meet, the bottom of the sign to the top of the sign covers an angle of 8 degrees (40 - 32).
Image a right triangle, A, B, C where line AB is the base, line AC is the height of the building, and BC is the hypotenuse and where angle A = 90 degrees, angle B = 32 degrees, and angle C = 58 degrees.
C
A B
Now image a second right triangle, A, B', D where line AB' is the base, same as the first triangle, line AD is the height of the building plus the height of the sign, and B'D is the hypotenuse, and where angle A = 90 degrees, angle B' = 40 degrees, and angle D = 50 degrees.
D
C
A B'
Note: B and B' are at the same point
We can use the law signs to find the length of B'C because we know the length of CD, 15 meters, the difference between the angles B and B', 40 degrees - 32 degrees, or 8 degrees, and the angle D, 50.
CD/Sin(8) = CB'/sin(50)
15/sin(8) = CB'/sin(50)
Cross multiply:
CB' = (15 * sin(50)) / sin(8)
CB' = 82.56 meters, Note: CB and CB' are the same line.
Now that we know the hypotenuse of the first triangle, A, B, C, we can find the height of the building again using the law of signs.
AC/sin(32) = CB'/sin(90)
AC/sin(32) = 82.56/sin(90)
Cross-multiply:
AC = (82.56 * sin(32))/sin(90)
AC = 43.75 meters
The height of the building to the nearest meter is 44 meters.
Questions?
