A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes.

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DesperatforanA

07.10.2020

Mathematics

Recall that $\sin^2x+\cos^2x=1$ .

This means

$\cos u=\sqrt{1-\sin^2u}=\sqrt{1-\dfrac19}=\dfrac{\sqrt8}3=\dfrac{2\sqrt2}3$
$cos v=sqrt{1-\sin^2v}=\sqrt{1-\dfrac1{16}}=\dfrac{\sqrt{15}}4$
$\sin(u+v)=\sin u\cos v+\sin v\cos u=\dfrac13\times\dfrac{\sqrt{15}}4+\dfrac14\times\dfrac{2\sqrt2}3=\dfrac{2\sqrt2+\sqrt{15}}{12}$

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