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Tuesday, 10 June 2014

# Pembahasan Latihan Soal Matematika 4

Question:
Consider the following figure!

The height of tower from above figure is ....

First, determine the distance between the sea level with the base tower. Use phytagorean theorem!
Because of the angle, 45 degrees, 45 degrees, and 90 degrees, then the triangle is right-angled isosceles. If the base and height of the triangle we let x, then:
$x^{2}+x^{2}=(1,2\sqrt{2})^{^{2}}km$
$2x^{2}=(1,2\sqrt{2})^{^{2}}km$
$2x^{2}=(2,88) km$
$x^{2}=1,44 km$
$x=1,2 km$
Next, determine the distance between the sea level with the top tower
According the ratio comparison of special angles in a triangle, known comparison side front corner of 30 degrees, 60 degrees, and 90 degrees are$x,x\sqrt{3},2x$, so:
$x= 1,2 km$
$x\sqrt{3}=1,2\sqrt{3}km$

The height of tower is the difference of distance between the sea level with the base tower and the distance between the sea level with the top tower, so that:
height of tower is $1,2\sqrt{3}-1,2$ km.