Question

question 24
determine the altitude (height) of the plane in the image below.
850 m
360 m
note: figure is not drawn to scale.
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Explanation:

Step1: Apply Pythagorean theorem

Let the height of the plane be $x$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 850$ m and $b = 360$ m, and $a=x$. So $x=\sqrt{c^{2}-b^{2}}$.

Step2: Calculate the value of $x$

$x=\sqrt{850^{2}-360^{2}}=\sqrt{(850 + 360)(850 - 360)}=\sqrt{1210\times490}=\sqrt{11^{2}\times10\times7^{2}\times10}=\sqrt{11^{2}\times7^{2}\times10^{2}} = 11\times7\times10=770$

Answer:

770