SOLUTION: A vertical pole XY is erected on a piece of lever ground. A student whose eye, E is 1.5m above the ground is standing at Z 12m away from Y the foot of the pole. If XEY = 50 degree

Algebra ->  Trigonometry-basics -> SOLUTION: A vertical pole XY is erected on a piece of lever ground. A student whose eye, E is 1.5m above the ground is standing at Z 12m away from Y the foot of the pole. If XEY = 50 degree      Log On


   

Question 1141856: A vertical pole XY is erected on a piece of lever ground. A student whose eye, E is 1.5m above the ground is standing at Z 12m away from Y the foot of the pole. If XEY = 50 degree. Use tables to calculate the height of the top of the pole above ground level. (Give your answer and correct to the nearest meter
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A vertical pole XY is erected on a piece of lever ground. A student whose eye, E is 1.5m above the ground is standing at Z 12m away from Y the foot of the pole. If XEY = 50 degree. Use tables to calculate the height of the top of the pole above ground level. (Give your answer and correct to the nearest meter
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What sort of tables?
Is his eye 12 m from the pole, or 12 m from point Y?
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Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Some of but NOT a finished solution:
Draw the described figure. YZ along the ground, YE a hypotenuse;
Triangle YZE.
On top of that triangle another sharing side YE with the on-the-ground triangle, triangle XYE.

YZ = 12;
ZE = 1.5
X is top of the pole. Y is on the ground.
m of angle YZE is 90 degrees.

YE=sqrt%281.5%5E2%2B12%5E2%29

sin%28EYZ%29%2F1.5=sin%2890%29%2FYE

sin%28EYZ%29=1.5%2Fsqrt%281.5%5E2%2B12%5E2%29
from which find
m of angle EYZ=+arcsin%281.5%2Fsqrt%281.5%5E2%2B12%5E2%29%29
and from that find
measure of angle XYE = 90-arcsin%281.5%2Fsqrt%281.5%5E2%2B12%5E2%29%29.

You want to solve for XY.
You would now have found known:
meas angle XYE;
meas angle YEX (fifty degree);
length YE;
AND YOU CAN COMPUTE ANGLE YXE having now already two of the upper triangles angle measures.

From there use Law Of Sines to find XY.