SOLUTION: Provide a sketch for this information. A measuring instrument is used at point P and Q on the same horizontal level to measure the angle of elevation of the top T of a hill. Given

Algebra ->  Trigonometry-basics -> SOLUTION: Provide a sketch for this information. A measuring instrument is used at point P and Q on the same horizontal level to measure the angle of elevation of the top T of a hill. Given      Log On


   

Question 1142029: Provide a sketch for this information.
A measuring instrument is used at point P and Q on the same horizontal level to measure the angle of elevation of the top T of a hill. Given that P is 5200m above sea level. PQ = 4000m and the angle of elevation of p and Q are 15degrees and 35degrees respectively, calculate the height of the mountain
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your diagram looks like this.

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P and Q are both 5200 meters above sea level.

triangles PMQ and PMB are formed.

angle MPQ is 15 degrees.

angle MQB is 35 degrees.

the height of MB is equal to x.

the length of QB is equal to y.

tan(15) = x / (4000 + y)

tan(35) = x / y

solve for x in both equations to get:

x = (4000 + y) * tan(15)

x = y * tan(35)

replace x in the first equation with y * tan(35) to get:

y * tan(35) = (4000 + y) * tan(15)

simplify to get y * tan(35) = 4000 * tan(15) + y * tan(15)

subtract y * tan(15) from both sides of the equation to get:

y * tan(35) - y * tan(15) = 4000 * tan(15)

factor out the y to get y * (tan(35) - tan(15)) = 4000 * tan(15)

divide both sides of the equation by tan(35) - tan(15) to get:

y = 4000 * tan(15) / (tan(35) - tan(15))

solve for y to get y = 2479.528227 meters.

in triangle QMX, solve for x to get x = 2479.528227 * tan(35) = 1736.184356 meters.

the height of the mountain is x + 5200 = 6936.184356 meters.